ELECTRICAL    ENGINEERING    TEXTS 

.ELECTEICAL 

MEASUREMENTS 


BY 
FRANK  A.  ,LAWS,  S.  B. 

PROFESSOR    OF    ELECTRICAL  ENGINEERING,  MASSACHUSETTS  INSTITUTE 

OF   TECHNOLOGY    AND  HARVARD  UNIVERSITY;    MEMBER  OF  THE 

AMERICAN    INSTITUTE    OF    ELECTRICAL    ENGINEERS,  ETC. 


FIRST  EDITION 


McGRAW-HILL  BOOK  COMPANY,  INC 
239  WEST  39TH  STREET.    NEW  YORK 


LONDON:  HILL  PUBLISHING  CO.,  LTD. 

6  &  8  BOUVERIE  ST.,  E.  C. 
1917 


COPYRIGHT,  1917,  BY  THE 
McGRAW-HiLL  BOOK  COMPANY,  INC. 


THE    MAPLE    PRESS    YORK    F»A 


PREFACE 

In  this  book  it  is  intended  to  give  a  general  treatment  of  the 
subject  of  electrical  measurements,  special  emphasis  being  placed 
on  those  matters  which  are  important  to  the  student  of  electrical 
engineering. 

In  preparing  a  book  of  this  character  one  has  to  consider,  not 
only  the  mature  reader  who  may  desire  a  compendium  of  methods 
together  with  certain  practical  suggestions,  but  the  student  who 
is  beginning  the  study  of  Electrical  Engineering  and  who  should 
acquire  early  in  his  course  a  sound  knowledge  of  the  process  of 
electrical  measurement.  This  knowledge  is  fundamental  not 
only  to  much  of  the  work  which  the  student  is  required  to  do  in 
the  dynamo  laboratory  as  a  matter  of  engineering  training,  but 
to  an  adequate  understanding  of  electrical  testing  as  it  is  en- 
countered in  the  practice  of  the  electrical  engineering  profession. 
In  the  preparation  of  the  text  this  second  class  of  readers  has 
been  particularly  in  mind. 

It  is  assumed  that  those  who  use  this  text  have  had  courses  in 
physics,  the  theory  of  electricity,  and  in  mathematics,  such  as 
are  given  to  third  year  students  in  technical  schools  of  the  first 
rank. 

The  choice  of  material  and  the  method  of  treatment  have  been 
determined  by  the  author's  experience  in  directing  for  many 
years  the  work  of  the  laboratory  for  Technical  Electrical  Meas- 
urements at  the  Massachusetts  Institute  of  Technology,  and  the 
book  is  intended  as  a  text  for  the  guidance  of  students  working  in 
such  a  laboratory  as  well  as  a  general  reference  book  on  the 
subject. 

It  is  expected  that  those  using  the  book  for  purposes  of  instruc- 
tion will  select  such  portions  as  are  best  suited  to  their  purposes, 
for  more  material  is  presented  than  can  be  utilized  in  both  the 
class  room  and  the  laboratory  in  the  time  which  can  properly  be 
allotted  to  this  particular  phase  of  electrical  engineering  instruc- 
tion. In  this  connection  it  is  suggested  that  interest  and  dis- 
cussion are  stimulated  if  the  laboratory  work  is  so  arranged  that 


37m 


vi  PREFACE 

the  various  members  of  the  class  while  engaged  with  the  same 
general  topic  carry  out  the  experimental  work  by  alternative 
methods. 

For  the  use  of  those  who  desire  a  more  detailed  discussion  of 
the  various  methods,  references  to  certain  important  papers  are 
appended  to  each  chapter.  While  no  attempt  had  been  made 
to  form  a  bibliography  of  the  subject  of  electrical  measurements 
it  is  thought  that  these  references  should  be  of  value  in  directing 
the  students'  attention  to  the  original  sources  of  information 
and  thus  assisting  him  to  a  broad  view  of  this  particular  part  of 
his  professional  training. 

The  various  commercial  instruments  described  in  the  text  have 
been  selected  simply  as  giving  good  illustrations  of  the  applica- 
tion of  the  particular  principles  under  discussion.  No  /attempt 
has  been  made  to  discuss  instruments  made  by  different  makers 
which  differ  merely  in  minor  details. 

The  author  wishes  to  thank  Professor  H.  E.  Clifford,  Gordon 
McKay  Professor  of  Electrical  Engineering  at  Harvard  Univer- 
sity and  the  Massachusetts  Institute  of  Technology,  for  his  con- 
tinued interest  in  the  work  and  for  the  many  and  valuable  sugges- 
tions which  he  has  made  during  its  preparation. 

F.  A.  LAWS. 

MASSACHUSETTS  INSTITUTE  OP  TECHNOLOGY, 
July  5,  1917. 


CONTENTS 

PAGE 

PREFACE v 

CHAPTER  I 

THE  MEASUREMENT  OF  CURRENT 1 

Classes  of  Instruments— GALVANOMETERS — The  Tangent  Gal- 
vanometer— The  Helmholtz  Galvanometer — The  Thomson  or 
Kelvin  Reflecting  Galvanometer — Magnetic  Shields — The  Needle 
System — Damping — Arrangement  of  the  Galvanometer  Coils — 
Galvanometer  Constant — Best  Form  of  Cross-section — Graded 
Coils — Relation  between  the  Galvanometer  Constant  and  the 
Resistance  of  a  Thomson  Galvanometer — The  Best  Resistance  for 
a  Thomson  Galvanometer — The  Sensitiveness  of  Reflecting  Gal- 
vanometers— Ampere  Sensitivity.  Microampere  Sensitivity — Rela- 
tion between  Time  of  Vibration  and  Current  Sensitivity — Normal 
Sensitivity — Volt  Sensitivity.  Microvolt  Sensitivity — Megohm 
Sensitivity — Design  for  a  Reflecting  Galvanometer — The  Broca 
Galvanometer — THE  MOTION  OF  THE  SUSPENDED  SYSTEM 
OF  A  GALVANOMETER — The  Equation  of  Motion — Nonoscil- 
latory  Deflection — Oscillatory  Deflection — Logarithmic  Decre- 
ment—Influence of  Damping  on  the  Time  of  Vibration— Crit- 
ical Damping — The  D'Arsonval  or  Moving-coil  Galvanome- 
ter— The  Magnets — Effect  of  Magnetic  Impurities  in  the  Coil — 
Suspensions — Effect  of  Changes  of  Temperature — Magnetic 
Damping — The  Critically  Damped  Moving-coil  Galvanometer — 
Current  and  Voltage  Sensitivity — Expression  for  the  Field  Re- 
quired to  Produce  Critical  Damping — Auxiliary  Damping — Pos- 
sible Adjustments — The  Einthoven  or  String  Galvanometer — The 
Duddell  Thermo-galvanometer — POINTS  TO  BE  CONSIDERED 
WHEN  SELECTING  A  GALVANOMETER — Sensitivity — Period — 
Damping — Resistance — Freedom  from  Effects  of  Mechanical 
Disturbances — Freedom  from  Stray-field  Effects — Definiteness 
of  Zero  Reading — Law  of  Deflection — Visibility  of  Suspended 
Parts — Accessibility  for  Repairs — Temperature  Effects — Optical 
System — THE  JULIUS  DEVICE  FOR  ELIMINATING  THE  EFFECTS  OF 
MECHANICAL  DISTURBANCES  ON  GALVANOMETERS — SHUNTS — The 
Ayrton-Mather  Universal  Shunt — AMMETERS — Moving-coil  Am- 
meters— Weston  Standard  Portable  Ammeter — Thermo-ammeters 
— The  Duddell  Thermo-ammeter — High-frequency  Ammeters — 
The  Parallel-wire  Ammeter — The  Use  of  High  Resistance  Wires — 
The  Utilization  of  the  Whole  Heat  Production — Sectionalized 


viii  CONTENTS 

PAGE 

Wires — SOFT-IRON  INSTRUMENTS — Magnetic-vane  Instruments — 
Weston  Soft-iron  Instruments — The  General  Electric  Co.'s  In- 
clined-coil Ammeter — THE  ELECTRODYNAMOMETER  AND  THE  CUR- 
RENT BALANCE — Secondary  Electrodynarnorneter.  Siemens  Dyna- 
mometer— Setting  up  the  Siemens  Electrodynamometer — The 
Law  of  the  Electrodynamometer — Astatic  Electrodynamometers — 
The  Irwin  Astatic  Electrodynamometer — Rewinding  an  Electro- 
dynamometer  to  Obtain  a  Given  Performance — Electrodyna- 
mometers for  Heavy  Currents — Wattmeter  Method  for  Measuring 
Large  Alternating  Currents — Agnew  Tubular  Electrodynamometer 
— Theory  of  the  Tubular  Electrodynamometer — The  Current 
Balance — Secondary  Current  Balances.  The  Kelvin  Balance — 
MEASUREMENT  OF  CURRENTS  IN  PERMANENTLY  CLOSED  CIRCUITS. 

CHAPTER  II 

THE  BALLISTIC  GALVANOMETER 99 

Checking  Devices — Precautions  in  Reading — The  Calibration  of  a 
Ballistic  Galvanometer — Theory  of  the  Undamped  Ballistic  Gal- 
vanometer— Formula  for  the  Kelvin  Galvanometer — Theory  of 
the  Damped  Ballistic  Galvanometer — The  Critically  Damped 
Ballistic  Galvanometer — The  Use  of  Shunts  with  the  Ballistic 
Galvanometer — The  Flux  Meter. 

CHAPTER  III 

RESISTANCE  DEVICES 128 

Resistance  Coils— Standard  Resistances — Resistance  Coils  for 
Alternating-current  Work— Tenth-ohm  Coils — One- ohm  Coils — 
Ten-ohm  Coils — One  Hundred-ohm  Coils — One  Thousand-ohm 
Coils — Five  Thousand-ohm  Coils — Ten  Thousand-ohm  Coils — 
Low-resistance  Shunts  for  Use  in  Alternating-current  Measure- 
ments— Resistance  Boxes — Dial  and  Decade  Arrangements — 
Multiple  Decade  Arrangements — Arrangements  for  Reducing  the 
Number  of  Coils  in  a  Decade — RHEOSTATS — Water  Rheostats — 
Water  Rheostats  with  Plate  and  Cylindrical  Electrodes — Wire- 
wound  Rheostats — Immersed-wire  Rheostats — Drop  Wires — Car- 
bon Compression  Rheostats. 

CHAPTER  IV 

THE  MEASUREMENT  OF  RESISTANCE 155 

Volt  and  Ammeter  Method — Substitution  Method — Direct-de- 
flection Method — Potentiometer  Method — Differential-galva- 
nometer Method — Kohlrausch's  Method  of  Using  a  Differential 
Galvanometer — Conditions  for  Balance — The  Wheatstone  Bridge 


CONTENTS  ix 

PAGE 

— Auxiliary  Apparatus — Keys — The  Galvanometer — The  Shunt — 
The  Null  Method  of  Making  a  Measurement — The  Deflection 
Method — Examples  of  Arrangements  of  Bridge  Tops — Calibration 
of  a  Resistance  Box — Compensation  for  Large  Thermo-e.m.f. — 
Slidewire  or  Divided-meter  Bridge — Resistances  at  Ends  of 
Bridge — Extension  Coils — Carey  Foster  Method  of  Comparing 
Two  Nearly  Equal  Coils — Determination  of  the  Resistance  per 
Unit  Length  of  the  Slide  Wire — Calibration  of  a  Slide  Wire — 
Carey  Foster  Method  of  Calibrating  a  Slide  Wire — Barus  and 
Strouhal  Method  for  Calibrating  a  Slide  Wire — Thomson-bridge 
Method  for  Calibrating  a  Slide-wire — Calibration  Corrections — 
General  Discussion  of  the  Wheatstone  Bridge — Galvanometer 
Current — The  Best  Resistance  for  a  Thomson  Galvanometer  When 
Used  with  a  Wheatstone  Bridge — Best  Position  for  the  Galva- 
nometer— Sensitiveness  Attainable  with  the  Wheatstone  Bridge — 
MEASUREMENT  OF  Low  RESISTANCES — Wheatstone  Bridge  Method 
— Thomson  Bridge  or  Kelvin  Double  Bridge — Expression  for 
Galvanometer  Current — Best  Resistance  for  a  Thomson  Galvan- 
ometer when  used  with  a  Thomson  Bridge — Sensitiveness  Attainable 
in  Measurements  with  the  Thomson  Bridge — Precision  Measure- 
ments with  the  Thomson  Bridge — Reeves  Method  for  Adjusting  the 
Ratio  Arms  to  Eliminate— Wenner  Method  of  Eliminating  the 
Effects  of  Lead  Resistances  and  a — Measurement  of  Resistances 
in  Permanently  Closed  Circuits — MEASUREMENT  OF  HIGH  AND 
INSULATION  RESISTANCES — Direct-deflection  Method — Precau- 
tions— Immersion — Absorption  Effects — Effect  of  Temperature — 
Insulation  Testing  by  Voltmeter — Loss  of  Charge  Method — Loss  of 
Charge  Method,  Using  Quadrant  Electrometer — Evershed  "Meg- 
ger"— MEASUREMENT  OF  INSULATION  RESISTANCES  OF  COMMER- 
CIAL CIRCUITS  WHEN  POWER  is  ON — Voltmeter  Method — North- 
rup  Method — Other  Methods  of  Measuring  Resistance  to 
Ground — THE  TEMPERATURE  COEFFICIENT  OF  ELECTRICAL  RE- 
SISTANCE— Mean  Temperature  Coefficient — Temperature  Coeffi- 
cient of  Resistance — Special  Case:  Temperature  Correction  for 
Copper — Measurement  of  Rise  of  Temperature — The  Resistance 
Pyrometer — RESISTIVITY,  CONDUCTIVITY — Resistivity-tempera- 
ture Constant — Relation  between  Resistivity  and  the  Tempera- 
ture Coefficient  of  Resistance — Per  Cent.  Conductivity — Resis- 
tivity of  Aluminum — Conductivity  Bridges — Hoopes  Conduc- 
tivity Bridge. 

CHAPTER  V 

THE  MEASUREMENT  OF  POTENTIAL  DIFFERENCE  AND  ELECTROMOTIVE 

FORCE 236 

Effect  of  Temperature — Multipliers — Electrodynamometer  Volt- 


x  CONTENTS 

PAGE 

meters — Hot-wire  Voltmeters — ELECTROSTATIC  INSTRUMENTS — 
The  Attracted-disc  Electrometer — The  Quadrant  Electrometer — 
The  Mechanical  and  Electrical  Zeros — General  Considerations — 
Electrostatic  Voltmeters — Use  of  a  False  Zero  Reading — Condenser 
Multipliers  for  Extending  the  Range  of  Electrostatic  Voltmeters — 
THE  SPARK-GAP  METHOD  OF  MEASURING  HIGH  PEAK  VOLTAGES — 
POTENTIOMETER  ARRANGEMENTS — Poggendorf's  Method  of  Com- 
paring a  Potential  Difference  and  an  Electromotive  Force — The 
Potentiometer — Practical  Arrangement  of  the  Potentiometer — 
Low-scale  Arrangement — Wolff  Potentiometer — The  Brooks  De- 
flection Potentiometer — The  "  Therm okraftfrei"  Potentiometer — 
Effect  of  Thermo-electromotive  Forces — Application  of  the  Poten- 
tiometer to  Alternating-current  Measurements — The  Drysdale 
Phase  Shifter — The  Drysdale-Tinsley  Alternating-current  Potenti- 
ometer— STANDARD  CELLS — The  Clark  Cell— Board  of  Trade  Cell — 
The  H  Cell— Materials  Used  in  Standard  Cells— The  Weston  or 
Cadmium  Cell — The  Weston  Secondary  Standard  Cell — Precau- 
tion in  Using  Standard  Cells. 

CHAPTER  VI 

POWER  MEASUREMENT 303 

The  Electrodynamometer  Wattmeter — Heating  Losses  in  Watt- 
meters— Compensation  for  Energy  Loss  in  the  Potential  Circuit — 
Grouping  of  Instruments — Errors  due  to  Local  Fields — Voltage 
between  Current  and  Potential  Coils — The  Effect  of  Reactance  in 
the  Potential  Circuit — Compensation  for  the  Inductance  of  the 
Potential  Circuit — Effect  of  Mutual  Inductance  between  Fixed  and 
Movable-coil  Circuits — Eddy-current  Errors — OTHER  METHODS 
OP  MEASURING  POWER — The  Three  Dynamometer  Method — The 
Three  Voltmeter  Method — The  Split-dynamometer  Method — 
Potier  Method  for  Power  Measurement — The  Electrostatic  Watt- 
meter— Sources  of  Error — Ryan  Power  Diagram  Indicator — 
POWER  MEASUREMENT  IN  POLYPHASE  CIRCUITS — Blondel's  Theo- 
rem— Designation  of  Wattmeter  Terminals — Two-phase  Three- 
wire  System — Two-wattmeter  Method — The  Polyphase  Watt- 
meter— Three-phase  Power  Measurement  by  Three  Wattmeters — 
The  Y-box — Four-wire  Three-phase  System. 

CHAPTER  VII 

MEASUREMENT   OF  INDUCTANCE  AND  CAPACITY 341 

STANDARDS  OF  INDUCTANCE — Standards  of  Mutual  Inductance — 
Campbell  Fixed  Standard  of  Mutual  Inductance — Variable 
Mutual  Inductances — Ayrton  and  Perry  Inductor — Brooks  Vari- 
able Inductor — STANDARDS  OF  CAPACITY — Secondary  Air  Conden- 


CONTENTS  xi 

PAGE 

sers — Working  Standards  of  Capacity — Condensers  on  Direct-cur- 
rent Circuits — Condensers  on  Alternating-current  Circuits — Mica 
Condensers — Paraffined  Paper  Condensers — METHODS  OF  MEAS- 
UREMENT— Determination  of  Capacity  in  Absolute  Measure — 
Direct-deflection  Method  for  Comparing  Capacities — Sources  of 
Error — The  Zeleny  Discharge  Key — Deflection  Method  Using  a 
Commutator — Thomson  Method  for  Comparing  Capacities — 
Gott  Method  for  Comparing  Capacities — Elementary  Methods  of 
Determining  Inductance  and  Capacity  by  Alternating  Currents — 
Capacity  Measurements — BRIDGE  MEASUREMENTS  OF  CAPACITY 
AND  INDUCTANCE — Conditions  for  Zero  Indication  of  Detector — 
De  Sauty  Method  for  Comparing  Capacities — Maxwell  Method  for 
Comparing  Inductances — The  Secohmmeter — The  Impedance 
Bridge — Capacity  Measurements — Determination  of  Phase  Angle 
of  Condenser — Determination  of  Equivalent  Capacity  and  Con- 
ductance of  Condenser  or  Short  Length  of  Cable — Bridge  for 
Measurement  of  Electrolytic  Conductivity — Wagner  Earth  Con- 
nection— Inductance  Measurements — The  Impedance  Bridge  with 
Four  Inductive  Arms — The  Anderson  Bridge — Effect  of  Dissi- 
pation of  Energy  in  the  Condenser — The  Mutual  Inductance 
Bridge — Effect  of  Eddy  Currents — Wilson  Method  for  Measuring 
Inductance — The  Measurement  of  Inductances  Containing  Iron — 
Measurement  of  Mutual  Inductance — Maxwell  Method  of 
Comparing  Mutual  Inductances — Measurement  of  Mutual  Induc- 
tance in  Terms  of  Capacity — SOURCES  OF  CURRENT — Vreeland  Os- 
cillator— The  Microphone  Hummer — Electrical  Resonators — 
Fleming  and  Dyke  Resonator — DEVICES  FOR  MAINTAINING  CON- 
STANT SPEED — The  Giebe  Speed  Regulator — The  Leeds  and 
Northrup  Automatic  Speed  Controller — The  Wenner  Speed  Con- 
troller— THE  VIBRATION  GALVANOMETER— Current  Sensitivity — 
Voltage  Sensitivity. 

CHAPTER  VIII 

INDUCTION  INSTRUMENTS 444 

The  Induction  Principle — Application  to  Measuring  Instruments — 
Ammeters  and  Voltmeters — Frequency  and  Temperature  Effects 
in  Westinghouse  Ammeter — The  Induction  Wattmeter. 

CHAPTER  IX 

ELECTRICITY  METERS 457 

Watt-hour  Meter — General  Discussion  of  Essential  Characteristics 
— Use  of  Watt-hour  Meters  on  Three-wire  Circuits — The  Use  of 
Commutating  Watt-hour  Meters  on  Alternating-current  Circuits — 
Lag  Coil — The  Induction  Watt-hour  Meter — The  Lag  Adjustment 


xii  CONTENTS 

PAGE 

— Light-load  Adjustment — Sources  of  Error  in  Induction  Watt- 
hour-Meters — Temperature  Errors — Frequency  Errors — Effect  of 
Wave  Forms — Effect  of  Voltage  Variations — Polyphase  Watt- 
hour  Meters — MERCURY  MOTOR  .METERS — The  Mercury  Ampere- 
hour  Meter — Ferranti  Ampere-hour  Meter — Sangamo  Meter — 
The  Sangamo  Ampere-hour  Meter — The  Mercury  Watt-hour 
Meter — METER  TESTING — Common  Sources  of  Inaccuracy — 
Methods  of  Testing — Load  Boxes — Portable  Standard  Watt-hour 
Meters — Fictitious  Loads  and  Arrangements  for  Phase  Shifting — 
Phase-shifting  Devices — Testing  Polyphase  Induction  Meters — 
Testing  of  Large  Direct-current  Watt- hour  Meters  on  Fluctuating 
Loads — DEMAND  INDICATORS — The  Wright  Maximum-demand 
Indicator — General  Electric  Type  W  Watt  Demand  Indicator — 
Ingalls  Relay  Demand  Indicator — The  General  Electric  M-2 
Demand  Indicator — Printometer — The  Westinghouse  R.  O.  De- 
mand Indicator. 

CHAPTER  X 

PHASE    METERS,    POWER-FACTOR   INDICATORS,    SYNCHROSCOPES    AND 

FREQUENCY  METERS 530 

Idle  Current  Meters — Tuma  Phase  Meter — Single-phase  Power- 
factor  Meters — Polyphase  Power-factor  Meters — Power-factor 
Charts — The  Lincoln  Synchronizer — Weston  Synchronizer — Hart- 
mann  and  Braun  Synchronizer — Synchronizing  Lamps-*-Siemens 
and  Halske  Arrangement  of  Phasing  Lamps — Frequency  Meters 
Resonating  Frequency  Meters — The  Induction  Frequency  Meter — 
Magnetic  Vane  Frequency  Meter. 

CHAPTER  XI 

GRAPHIC  RECORDING  OR  CURVE  DRAWING  INSTRUMENTS 552 

Direct  Acting  Instruments — Relay  Instruments. 

CHAPTER  XII 

INSTRUMENT  TRANSFORMERS 562 

Potential  Transformers — Current  Transformers — Power  Measure- 
ments— General  Considerations — Current  Transformers — Theory 
of  the  Current  Transformer — Theory  of  Potential  Transformer — 
Effect  of  Phase  Angles  in  Three-Phase  Power  Measurements — Use 
of  Transformers  with  Watt-hour  Meters — DETERMINATION  OF  THE 
RATIOS  AND  PHASE  ANGLES  OF  INSTRUMENT  TRANSFORMERS — 
Ratio  and  Phase  Angle  of  Current  Transformer — Ratio  and  Phase 
Angle  of  Potential  Transformers — Companson  Tests  of  Instru- 
ment Transformers. 


CONTENTS  xiii 

CHAPTER  XIII 

.  PAGE 

THE  CALIBRATION  OF  INSTRUMENTS 593 

Accuracy  and  Precision — Calibration  Before  and  After  Tests — 
Choice  of  Instruments — Errors  of  Reading — MECHANICAL  ERRORS 
— Friction — Springs — Balancing — Scale  Errors — Corrosion — ELEC- 
TRICAL AND  MAGNETIC  ERRORS — Shunts — Millivoltmeter  Leads — 
Thermo-electromotive  Forces — Effect  of  External  Tempera- 
tures— Internal  Heating  Errors — Stray  Fields — Electrostatic  At- 
traction— Eddy  Currents — Current  Distribution — Frequency  and 
Wave  Form — Use  of  Transformers — Direct- current  Instruments — 
Voltmeter  Calibration  by  Standard  Cell — Ammeter  Calibration — 
Calibration  by  Means  of  Potentiometer — Alternating-current  Am- 
meters and  Voltmeters — The  Northrup  Alternating-  and  Direct- 
current  Comparator — Wattmeters. 

CHAPTER  XIV 

DETERMINATION  OF  WAVE  FORM 612 

Contact  Method  for  Determining  Wave  Forms — Use  of  Potenti- 
ometer Principle — Integrating  Methods  for  Determining  Wave 
Form — E.m.f.  Waves — Flux  Waves — Use  of  Condenser  and  Syn- 
chronous Commutator — Determination  of  the  Average  Values  of 
Potential  Difference  and  Current  Waves — Determination  of  Form 
Factor — The  Oscillograph — Theory  of  the  Oscillograph — The  Elec- 
trostatic Oscillograph — Adjustment  of  Electrostatic  Oscillograph — 
The  Braun  Tube — Permanent  Records  by  Braun  Tubes — Electro- 
static Tubes — General  Considerations — WAVE  ANALYSIS — Runge 
Method  of  Grouping  Terms — Sine.  Terms — Cosine  Terms — ILLUS- 
TRATION OF  THE  USE  OF  A  TWELVE-POINT  SCHEDULE  FOR  THE 

ANALYSIS  OF  WAVES  CONTAINING  ONLY  ODD  HARMONICS — Fischer- 
Hinnen  Method  of  Analysis — Harmonic  Analyzers — Experimental 
Analysis:  Laws  Method. 

CHAPTER  XV 

CABLE  TESTING 672 

FAULT  LOCATION — Location  of  Grounds  and  Crosses — Blavier 
Test— The  Earth  Overlap  Test— The  Volt-ammeter  Test— Loop 
Tests — Two-ammeter  Loop  Test — Murray  Loop  Test — Varley 
Loop  Test — Determination  of  the  Total  Resistance  of  the  Defect- 
ive Conductor — Fisher  Loop  Test — Corrections  for  Conductors 
of  Different  Diameters — Locating  Faults  in  Underground  High- 
tension  Cables — Location  of  Total  Disconnection — Breakdown 
Tests  of  High-voltage  Cables — Measurement  of  Peak  Voltage. 

LEGAL  DEFINITIONS  OF  THE  ELECTRICAL  UNITS  IN  THE  UNITED  STATES  705 
INDEX  .   707 


ELECTRICAL  MEASUREMENTS 

CHAPTER  I 
THE  MEASUREMENT  OF  CURRENT 

Classes  of  Instruments. — Electrical  measuring  instruments 
may  be  divided  into  two  classes: 

1.  Absolute  instruments. 

2.  Secondary  instruments. 

An  absolute  instrument  is  one  so  designed  and  built  that  it 
gives  results  expressed  in  the  absolute,  or  c.g.s.,  system  of  units. 
This  implies  that  the  numbers  of  turns  in  the  coils  and  all  the 
dimensions  which  are  electrically  important  have  been  deter- 
mined, so  that  the  factor  which  connects  the  force  or  the  turning 
moment  acting  on  the  movable  member,  and  the  numerical  value 
of  the  quantity  under  measurement  can  be  calculated. 

A  secondary  instrument  is  one  so  constructed  that  the  relation 
between  its  indications  and  the  quantity  under  measurement 
must  be  established  experimentally;  that  is,  the  instrument  must 
be  calibrated. 

Examples  of  absolute  instruments  are  the  tangent  galvan- 
ometer and  the  Rayleigh  current  balance  (see  page  89).  The 
ordinary  portable  ammeters,  voltmeters,  and  wattmeters  are 
examples  of  secondary  instruments. 

Absolute  instruments  are  not  adapted  for  general  use  and  are 
rarely  employed  outside  of  such  establishments  as  the  Bureau 
of  Standards,  the  National  Physical  Laboratory  or  the  Reichsan- 
stalt.  Their  particular  field  of  usefulness  is  in  the  determination 
of  the  fundamental  electrical  constants;  for  example,  the  inter- 
national ampere. 

GALVANOMETERS 

The  Tangent  Galvanometer. — This  is  an  absolute  instrument. 
It  consists  essentially  of  a  circular  coil  of  insulated  wire,  having 


2  ;<;/.  KC  TR  ic  A  L  ME;A  s  u  RE  MEN  TS 

a  radius  which  is  large  compared  with  the  dimensions  of  its  cross- 
section,  together  with  a  small  magnetic  needle  which  is  so  sus- 
pended at  the  center  of  the  coil  that  it  can  move  about  a  vertical 
axis.  The  needle  is  provided  with  a  pointer  which  moves  over 
a  scale  graduated  in  degrees.  The  coil  is  so  placed  that  its  plane 
is  vertical  and  in  the  magnetic  meridian.  When  no  current  is 


FIG.  1. — Tangent  galvanometer. 

flowing,  the  pointer  stands  at  zero  for  the  needle  is  then  con- 
trolled by  the  horizontal  component  of  the  local  magnetic  field,  H. 
On  the  passage  of  a  current  the  coil  sets  up  a  magnetic  field, 
which  at  the  needle  is  perpendicular  to  the  plane  of  the  coil  and 
of  magnitude 


where  n  is  the  number  of  turns  in  the  coil,  r  the  mean  radius  of 
the  coil  and  /  the  current  in  absolute  units.     The  needle  will  turn 


THE  MEASUREMENT  OF  CURRENT  3 

through  an  angle  9  and  take  up  a  position  along  the  resultant  of 

Fandtf 

Then 

F  2TTH    T 

tan  6  =  n  =-  Hr  I 
or 

TT 

I  =  —  tan  0  in  absolute  units  (1) 


-j  r\  TT 

I  =  -—  tan  0  in  amperes  (la) 


The  quantity  -      depends  on  the  dimensions  of  the  instrument 

and  is  the  strength  of  field  at  the  center  of  the  coil  due  to  unit 
current.     It  is  frequently  called-  the  gal- 
vanometer constant  of  the  coil  and  de- 
noted by  G. 

In  this  elementary  demonstration  it  has    H 
been  assumed  that: 

1.  The  coil  is  perfectly  circular. 

2.  The   mean   radius   of  the  windings 

correctly  represents  the  effective  radius.         Fl«-  2. — Fields  at 
o     mi_  '          ji     •  <i  -u  needle  of  tangent  galva- 

3.  The  needle  is  exactly  at  the  center      nometer. 

of  the  coil,  and  the  field  acting  on  a  finite 

needle  is  the  same  as  that  at  the  mathematical  center  of  the 

coil. 

4.  The  needle  is  in  a  uniform  field  and  consequently  as  it 
deflects,  its  poles  do  not  swing  into  a  field  of  strength  differing 
from  that  at  its  zero  position. 

5.  The  plane  of  the  coil  is  in  the  magnetic  meridian  and  truly 
vertical. 

6.  The  factor  H,  or  the    horizontal    intensity  of    the    local 
magnetic  field,  has  been  determined  at  the  place  occupied  by  the 
instrument  and  is  constant. 

7.  Only  magnetic  forces  act  on  the  needle;  that  is,  there  is  no 
friction  and  no  torsional  rigidity  in  the  suspension. 

In  a  careful  study  of  the  instrument  it  would  be  necessary  to 
discuss  each  of  these  items  and  to  determine  the  numerical  effect 


4  ELECTRICAL  MEASUREMENTS 

on  the  measured  value  of  the  current  of  the  unavoidable  de- 
partures from  the  assumed  conditions. 

In  absolute  electrical  measurements  this  part  of  the  work  often 
calls  for  mathematical  ability  of  a  high  order.. 

The  Helmholtz  Galvanometer. — In  this  instrument  the  needle 
is  suspended  on  the  axis  midway  between  two  equal  coils,  whose 
distance  apart  is  equal  to  their  radius. 


• 


FIG.  3. — Helmholtz  tangent  galvanometer. 

The  reason  for  this  construction  is  that  it  renders  the  field  in 
which  the  needle  swings  very  uniform,  so  that  the  correction  for 
the  finite  length  of  the  needle  is  much  reduced. 

This  arrangement  of  coils  is  frequently  employed  in  other 
instruments  where  a  uniform  magnetic  field  is  desired. 

These  absolute  galvanometers  depend  for  their  directive  force 
on  the  horizontal  component  of  the  local  field  at  the  place  where 


THE  MEASUREMENT  OF  CURRENT  5 

they  are  used.  This  quantity  is  subject  to  great  and  erratic  varia- 
tions due  to  the  proximity  of  electric  cars,  feeders,  and  struc- 
tural iron  work,  and  as  it  enters  as  a  direct  factor,  present-day 
conditions  have  rendered  these  instruments  practically  useless. 

Any  of  these  absolute  galvanometers  will  be  reduced  to  sec- 
ondary forms,  if,  in  the  attempt  to  gain  sensitiveness,  the  coils 
are  brought  close  to  the  needle. 

The  Thomson  or  Kelvin  Reflecting  Galvanometer.4 — This 
form  of  galvanometer  is  the  most  sensitive  instrument  for  the 


FIG.  4. — The  original  Thomson  galvanometer  used  on  board  the  Niagara 
in  1858,  the  first  instrument  by  which  a  signal  was  received  through  a 
transatlantic  cable. 

detection  and  measurement  of  direct  currents.  It  was  invented 
by  Lord  Kelvin  (then  "Professor  William  Thomson)  for  use 
originally  as  a  signalling  device  in  submarine  cable  work.  It 
had  been  noticed  that  signals  when  transmitted  through  the  short 
submarine  cables  then  in  use  (1854)  lost  their  sharpness  and  in 
some  of  the  experiments  became  unintelligible.  The  first  ade- 
quate explaAtion  of  this  was  given  by  Prof essor  Thomson  in  1854. 
He  showed  that  it  was  due  to  the  electrostatic  capacity  and  resist- 


6  ELECTRICAL  MEASUREMENTS 

ance  of  the  cable  and  demonstrated  that,  after  the  key  at  the 
sending  end  is  depressed,  a  definite  time,  a,  must  elapse  before  any 
current  is  received  at  the  far  end,  that  the  received  current  then 
gradually  rises,  attaining  90  per  cent,  of  its  full  value  only  after  the 
lapse  of  a  time  equal  to  10a  and  that  when  the  key  is  released  the 
received  current  gradually  falls  to  zero.  He  also  showed  that  the 
time  which  must  elapse  before  any  signal  is  received  depends 
upon  the  square  of  the  length  of  the  cable.  These  were  weighty 
matters,  for  "the  possibility  of  a  transatlantic  cable  was  then  under 
discussion.  Having  demonstrated  the  shape  of  the  " arrival" 
curve,  Professor  Thomson  invented  his  galvanometer  as  a  form 
of  receiving  instrument  adapted  to  cope  with  these  difficulties 
and  render  an  Atlantic  cable  an  economic  success  by  increasing 
the  speed  of  signalling.1  * 

What  he  desired  was  an  instrument  which  would  be  deflected 
by  minute  currents  and  follow  their  every  fluctuation.  The 
original  instrument  used  on  the  frigate  Niagara  in  1858  is  shown 
in  Fig.  4. 

The  essential  features  of  the  Thomson  galvanometer  are: 

1.  A  very  small  and  light  movable  magnetic  system  delicately 
suspended  within  a  coil  so  proportioned  that  its  turns  are  in 
close  proximity  to  the  needle. 

2.  A  small  needle,  controlled  by  the  combined  action  of  the 
local  magnetic  field  and  the  field  due  to  a  permanent  magnet. 

3.  The  magnification  of  the  motion  of  the  needle  by  the  use 
of  a  beam  of  light  as  an  index.     (A  small  concave  mirror  is 
attached  to  the  needle  and  throws  an  image  of  the  filament  of 
an  incandescent  lamp  on  a  graduated  scale  from  which  the  de- 
flections are  read.     The  equivalent  of  a  very  long  pointer  with 
a  small  moment  of  inertia  is  thus  obtained.     If  a  plane  mirror 
is  used,  the  reading  is  effected  by  a  telescope  and  scale.) 

In  the  older  forms  of  the  instrument  a  simple  magnetic  needle 
was  used.  This  was  cemented  to  the  back  of  the  mirror  which 
was  suspended  by  a  very  short  silk  fiber  in  a  tube  of  diameter 
slightly  greater  than  that  of  the  mirror.  The  tube  was  closed 
at  one  end  by  a  piece  of  plate  glass  and  at  the  other  by  a  movable 
plug.  As  the  suspended  system  swung  in  a  constricted  space 
its  motions  were  damped  by  air  friction. 

*  Numbers  refer  to  references  at  end  of  chapter. 


THE  MEASUREMENT  OF  CURRENT 


This  simple  form  of  instrument  is  unsatisfactory,  for  it  is 
not  possible  to  attain  an  exceedingly  high  degree  of  sensitivity 
owing  to  the  loss  of  effective  space  near  the  needle,  which  results 
from  putting  a  comparatively  large  mirror  within  the  coil.  The 
torsion  of  the  short  suspension  is  also  troublesome.  More  im- 
portant still  is  the  fact  that  the  usable  sensitivity  is  limited 
by  the  variability  of  the  local  field, 
due  to  outside  magnetic  disturb- 
ances. 

The  galvanometer  being  of  funda- 
mental importance  in  all  sorts  of 
electrical  testing,  later  experimenters 
have  devoted  much  time  to  the  im- 
provement of  the  details  of  the 
Thomson  type  of  instrument,  the 
desire  being  to  attain  a  very  high 
degree  of  sensitivity,  freedom  from 
outside  magnetic  disturbances,  a 
minimum  but  definite  torsional  con- 
trol due  to  the  suspension,  propor- 
tionality of  scale  reading  to  current, 
and  convenience  of  adjustment. 

A  form  of  Thomson  galvanometer 
in  which  a  simple  magnetic  system 
is  used,  is  shown  in  Fig.  5.  The 
needle  is  controlled  and  held  in  its 
zero  position  by  the  combined  action 
of  the  local  field  and  the  magnet  M. 


FIG.  5. — Simple  Thomson 
galvanometer.  Very  suscep- 
tible to  variations  of  the 
local  field. 


The  amount  of  the  control  and  thus  the  sensitivity,  as  well 
as  the  position  of  the  zero  reading  of  the  instrument  may  be 
altered  by  raising  or  lowering  M  and  turning  it  in  azimuth. 

A  simple  instrument  like  this  one  is  no  longer  useful,  for 
under  conditions  now  well-nigh  universal,  the  local  magnetic 
field  is  subject  to  such  erratic  variations  both  of  magnitude  and 
direction  that  neither  the  zero  nor  the  deflected  readings  can  be 
taken  with  certainty.  This  trouble  increases  as  the  sensitivity 
of  the  galvanometer  is  raised  by.  ad  justing  the  magnet  M.  The 
difficulties  may  be  minimized  in  two  ways: 

1.  A  truly  astatic  needle  system  may  be  used. 


8 


ELECTRICAL  MEASUREMENTS 


Suspension  Fibre 


2.  Magnetic  shields  may  be  employed. 

An  astatic  suspended  system  is  an  arrangement  of  two  sets  of 
magnets  of  equal  moment  lying  in  the  same  plane  and  rigidly 
connected.  The  north  poles  of  the  upper  element  are  directly 
over  the  south  poles  of  the  lower  element.  A  perfect  system 
of  this  sort  if  placed  in  a  uniform  field  will  experience  no  directive 
force,  and  it  i§  necessary  to  resort  to  the  use  of  a  controlling  mag- 
net. This  magnet  is  placed  in  a  horizontal  position,  usually 
above  the  system,  and  creates  a  field  which  is  stronger  at  the 
upper  than  at  the  lower  needles.  The  con- 
trolling force  becomes  less  as  the  fields  at  the 
upper  and  lower  needles  approach  equality. 

It  will  be  seen  that  fluctuations  of  H,  the 
local  field,  will  affect  the  directive  fields  at 
the  upper  and  lower  needles  equally  and  have 
no  influence  on  the  sensitiveness  or  the  zero 
reading  of  the  instrument. 

In  practice,  it  is  not  possible  to  adjust  the 
two  sets  of  magnets  so  that  they  are  exactly 
in  the  same  plane,  nor  is  it  possible  to  make 

a  their  moments  exactly  equal;  so  the  theoretic- 

Mirror  aiiy  perfect  system  cannot  be  realized.     The 

actual  system  will  have  a  small  resultant 
polarity  and  when  it  is  suspended  the  needles 
will  take  up  an  approximately  east  and  west 
direction.  Such  a  system  will  not  be  free 
from  the  effects  of  variations  of  the  local  field. 
Again,  the  magnetism  of  so-called  permanent 
magnets  gradually  deteriorates  so  that  the 
system  cannot  be  expected  to  remain  properly 
magnetized  even  though  its  initial  adjustment 
is  perfect.  For  this  reason,  some  better  expedient  has  been 
sought  and  recourse  has  been  had  to  magnetic  shielding. 

Magnetic  Shields.2 — In  order  that  a  galvanometer  may  be 
effectively  protected  from  variations  of  the  local  field  by  means 
of  iron  shields,  it  must  be  of  small  size  so  that  the  volume  of 
the  space  to  be  shielded  is  reduced  to  a  minimum.  The  shields 
may  be  either  spherical  or  cylindrical;  for  mechanical  reasons  the 
latter  form  is  to  be  preferred.  The  cylindrical  shields  are  left 


«-  Straight  Glass  or 
Quartz  Shank 


FIG.  6.— Astatic 
needle  system. 


THE  MEASUREMENT  OF  CURRENT 


9 


open  at  the  ends  and  the  diameter  is  made  small  compared  with 
the  length;  for  instance,  if  the  internal  diameter  is  2  or  3  cm.,  the 
length  may  very  well  be  about  30  cm.  See  Figs.  7  and  10. 

The  shielding  ratio,  that  is,  the  ratio  of  the  strength  of  the  ex- 
ternal local  field  to  the  corresponding  field  within  the  inner  shield 
is  greatly  affected  by  the  arrangement  of  the  iron.  If  the  iron  is 
all  concentrated  in  a  single  cylindrical  shield,  having  an  outside 
radius  five  times  the  inner  radius,  the  shielding  ratio  will  be  about 
98  per  cent,  of  that  for  a  shield  of  infinite  thickness.  If  a  single 
shield  of  permeability  202  be  used,  the  maximum  possible  shield- 
ing ratio  is  about  50.  This  shows  the  futility  of  trying  to  thor- 
oughly protect  a  galvanometer  by  a  single  shield  of  great  weight. 

If  a  given  weight  of  iron  is  used  in  several  concentric  shields, 
with  air  spaces  between  them,  its  effectiveness  is  vastly  increased. 

Given  the  innermost  and  outermost  radii  of  a  system  of  three 
shields,  the  shielding  ratio  is  a  maximum  when  the  radii  of  the 
shells  are  in  geometrical  progression. 

Cyclic  annealing  of  the  shields  at  high  temperatures  materially 
increases  their  effectiveness  through  an  increase  of  the  perme- 
ability. The  following  experimentally  determined  values  give  an 
idea  of  the  protection  afforded  by  a  multiple  shield.  No  joints 
or  lateral  openings  are  allowable. 

DATA  FOR  THREE  SHIELDS  OF  CAST  SILICON  STEELS 
Length  29.3  cm. 


Inner  radius, 
centimeters 

Outer  radius, 
centimeters 

Weight, 
grams 

Shield  No. 
Shield  No 

1  

2 

2.55 

4  40 

3.55 
5  45 

1,875 
7,500 

Shield  No. 

3  

8.25 

10.45 

26,900 

SHIELDING  RATIOS  OBTAINED  BY  USING  THE  ABOVEJ 


Shields  used 

Shielding  ratios 

Before  annealing 

After  annealing 

1 

1+2 

1+2+3 

18.62 
240.4 
2,900.0 

20.6 
317.6 
4,274.0 

10 


ELECTRICAL  MEASUREMENTS 


A  set  of  five  shields  cut  from  ordinary  soft  iron  water  pipes, 
and  annealed,  gave  the  results  quoted  below. 

DATA  FOR  FIVE  SHIELDS  OF  SOFT  IRON  PIPE 
Length  of  shields  30  cm. 


Inner  radius, 
centimeters 

Outer  radius, 
centimeters 

Weight, 
grams 

Shield  No 

1 

2.65 

3.0 

1,530 

Shield  No. 
Shield  No. 
Shield  No. 

2  
3  
4 

3.90 
5.20 
6  45 

4.45 
5.7 
7.05 

3,120 

4,260 
6,130 

Shield  No. 

5  

8.95 

9.7 

9,650 

SHIELDING  RATIOS  OBTAINED  BY  USING  THE  ABOVE 


Shields  used 


Shielding  ratios 


1 

1+2 
1+2+3 
1+2+3+4 
1+2+3+4+5 


19.3 
104.1 
252.0 
723.1 

2,724.8 


These  figures  show  that  a  Thomson  galvanometer  can  be  ren- 
dered practically  immune  from  the  effects  of  local  field  variation 
by  the  use  of  multiple  shields  with  air  spaces. 

A  commercial  form  of  galvanometer  in  which  spherical  shields 
are  employed  is  shown  in  Fig.  7. 

A  simple  and  effective  instrument,  the  one  from  which  the 
data  concerning  the  shields  were  taken,  is  shown  in  Fig.  10  on 
page  22. 

Under  present-day  conditions  it  is  useless  to  attempt  to  employ 
an  unshielded  Thomson  galvanometer. 

Suspensions. — In  Thomson's  original  instrument,  the  needle 
system  was  suspended  by  a  single  silk  fiber.  This  does  well 
enough  for  instruments  of  moderate  sensitivity.  When  the  high- 
est sensitivity  is  desired,  the  controlling  field  is  reduced  to  a 
minimum.  The  torsional  properties  of  the  suspension  fiber  then 
become  important .  Silk  fiber  suspensions  are  exceedingly  trouble- 
some for  they  are  greatly  affected  by  changes  of  hygrometric  con- 


THE  MEASUREMENT  OF  CURRENT 


11 


ditions,  the  result  being  a  continual  shifting  of  the  zero  point. 
To  remove  this  trouble,  C.  Vernon  Boys  introduced  the  use  of 
quartz-fiber  suspensions.3 

Quartz  when  melted  is  very  viscous  and  may  readily  be  drawn 
into  long  threads  of  uniform  cross-section.  Intrinsically,  quartz 
fibers  are  very  stiff  but  this  is  compensated  for  by  their  great 
strength  which  permits  the  use  of  exceedingly  fine  threads.  A 
fiber  0.0014  cm.  in  diameter  breaks  under  a  weight  of  about 
10  gm.  and  may  be  used  to 
carry  5  gm.;  finer  threads 
break  at  even  higher  stresses 
per  unit  area.  Fibers  as  long 
as  8  or  10  cm.  may  be  em- 
ployed for  galvanometer  sus- 
pensions.* 

It  is  found  that  with  quartz 
fibers  the  twist  produced  by  a 
given  turning  moment  is  ac- 
curately proportional  to  the 
moment  and  independent  of 
the  previous  history  of  the 
thread;  this  very  important 
property  allows  quartz-fiber 
suspensions  to  be  used  in  many 
sorts  of  instruments  where  a 
delicate  torsional  control  is  de- 
sired. 

The  Needle  System.— The 
system  must  be  light  with  the 
masses  symmetrically  placed 
with  respect  to  the  axis  of  rotation.  For  this  reason  the  shank 
carrying  the  needle  and  the  mirror  (be  in  Fig.  6)  must  be  per- 
fectly straight.  A  very  slender  glass  or  quartz  rod  such  as  is 
used  for  this  purpose  will  be  straightened,  if,  while  held  verti- 
cally under  the  tension  of  a  weight,  it  is  stroked  up  and  down 
with  a  yellow  gas  flame. 

*The  manipulation  of  fused  quartz  is  discussed  in  THRELFALL'S  book 
"  On  Laboratory  Arts,"  p.  196.  Quartz  fibers  are  now  articles  of  commerce 
and  may  be  obtained  of  the  Hanovia  Chemical  Co.,  New  York  City. 


FIG.  7. — Du  Bois-Rubens  shielded 
galvanometer. 


12  ELECTRICAL  MEASUREMENTS 

Symmetry  is  essential  in  order  that  mechanical  vibrations  may 
not  produce  excessive  disturbances  of  the  needle  system  and  thus 
render  difficult  the  reading  of  the  instrument.  The  moment  of 
inertia  of  the  non-magnetic  parts  of  the  system  should  be  reduced 
to  a  minimum,  so  the  mirror  must  be  small  and  light.  It  may 
be  cut  from  a  (silvered)  cover  glass  such  as  is  used  on  microscope 
slides. 

Each  member  of  an  astatic  system  may  consist  of  six  or  seven 
magnets.  Glass-hard  tungsten  steel  is  used  for  the  magnets 
which  may  be  about  1.2  mm.  long  and  0.2  mm.  or  less  in  diameter. 
The  magnets  are  attached  to  the  shank  by  minute  drops  of  shellac. 
To  preserve  the  symmetry  of  the  system  the  magnets  are  placed 
on  both  sides  of  the  shank.  The  total  mass  of  a  system  con- 
structed with  great  care,  for  use  in  research  work,  may  be  as 
small  as  6  or  7  mg.  Such  a  very  light  system  will  be  over-damped 
by  the  air  friction. 

Damping. — In  order  to  economize  time,  all  galvanometers 
should  be  properly  damped  so  that  they  will  come  promptly  to 
rest.  The  various  devices  used,  such  as  damping  vanes  or  in 
moving  coil  galvanometers,  damping  loops,  are  arrangements  for 
quickly  dissipating  the  energy  of  motion  of  the  movable 
system. 

Arrangement  of  the  Galvanometer  Coils. — In  order  to  attain 
a  high  sensitivity  the  windings  must  be  so  disposed  that  they 
produce  the  maximum  field  at  the  needle.  Having  given  a  defi- 
nite length  of  wire  of  a  certain  size,  it  will  be  most  effective 
when  used  on  an  astatic  galvanometer.  For  suppose  it  to  be 
wound  in  a  coil  adapted  to  a  single-needle  instrument,  the  outer 
layers  will  be  at  a  considerable  distance  from  the  needle  and 
therefore  their  effectiveness  will  be  small.  If  an  astatic  system 
is  used,  these  outer  layers  may  be  taken  off  and  wound  in  coils 
which  closely  surround  and  act  on  the  lower  member  of  the  needle 
system.  Thus  the  wire  as  a  whole  is  brought  into  a  more  advan- 
tageous position  and  the  sensitivity  of  the  instrument  increased. 

An  additional  advantage  is  derived  from  winding  the  wire  on 
four  rather  than  on  two  spools.  For,  to  a  certain  extent,  the 
galvanometer  resistance  may  be  changed  to  suit  the  work  in 
hand  by  connecting  the  four  coils  in  series,  series-parallel  or  in 
parallel. 


THE  MEASUREMENT  OF  CURRENT 


13 


Galvanometer  Constant. — It  is  natural  to  wind  the  coils  so 
that  their  cross-sections  will  be  rectangular.  Let  n'  be  the  num- 
ber of  turns  of  wire  per  square  centimeter  of  cross-section,  the 
other  quantities  being  denned  by  Fig.  8.  Then,  if  the  coil  is 
wound  throughout  with  the  same  size  of  wire  the  field  at  its 
center  due  to  unit  current  is 


G 


-x- 


FIG.  8. — Pertaining  to  demonstration  for  galvanometer  constant. 


For,  consider  the  filament  of  current,  dx  dy,  the  coordinates  of 
whose  trace  on  the  plane  of  the  paper  are  x  and  y.  The  magnetic 
force  at  the  center  of  the  coil  due  to  the  length  ds  of  this  filament 
when  conveying  unit  current,  will  by  the  elementary  laws  of 
electromagnetic  action  be  perpendicular  to  -the  radius  vector  of 
the  point,  x,  y,  and  have  for  its  value 

n'dsdydx 


When  resolved  along  the  axis  this  becomes 


14  ELECTRICAL  MEASUREMENTS 

n'dsdydx  y  _ 

"a-H-  y2    '  "  Vxz~+y*' 
and  for  the  whole  filament  is 

2irriy2dydx 


Therefore,  if  c  is  the  mean  radius  of  the  coil 


,fb  Cc+a      y^dydx 

G  =  2irri  I  -  =  4irn'b  log€ 

J-Jc-a    (x*  +  y*)V  3£ 

but 


8 

cot  ~ 
loge  - 

cot2 

Theoretically,  there  is  a  best  ratio  of  total  breadth  to  radius 
for  the  coil.  If  the  coil  has  a  fixed  volume  and  it  be  assumed  that 
the  diameter  of  the  core  is  zero,  G  will  be  a  maximum  when  ft  = 
30°.  8.  If  the  area  of  the  cross-section  be  fixed,  a  given  number 
of  turns  of  wire  of  a  definite  diameter  will  render  G  a  maximum 
when  (8  =  16°.66. 

Best  Form  of  Cross-section.  —  Theoretically,  the  rectangular 
form  of  cross-section  is  not  the  best.  With  a  definite  length  of 
wire  of  a  certain  size,  the  volume  of  the  coil  and  its  resistance  are 
fixed.  The  question  is,  how  shall  this  wire  be  arranged  so  that 
it  will  produce  the  maximum  effect  at  the  needle? 

The  effect  at  the  needle  of  a  unit  length  of  wire,  bent  into  an 

sin    a 
arc  of  a  circle  and  carrying  unit  current,  is  F  =  —  ^  —  where  r 

and  a  are  the  polar  coordinates  of  the  traces  of  the  wire  on  a  plane 
including  the  axis.  The  origin  of  coordinates  being  the  axis  of 

the  coil  and  the  coil  center,  call  —  ^  —  the  efficacy  of  a  unit  length 
of  wire,  denoted  by  ev.  Then  every  unit  length  of  wire  whose 
traces  are  on  the  curve  r2  =  —  sin  a,  where  ev  has  a  definite  value, 

Cv 

will  produce  the  same  effect  at  the  center  of  the  coil.     Suppose 


THE  MEASUREMENT  OF  CURRENT  15 

the  wire  has  been  so  wound  that  the  boundary  of  the  cross-section 
of  th<R  coil  is  given  by  r2  =  sin  a,  where  ev  has  some  particular 

6V 

numerical  value.  If  an  attempt  be  then  made  to  alter  the  form 
of  the  cross-section  by  changing  the  position  of  a  portion  of  the 
wire,  the  field  at  the  needle  will  be  reduced,  for  the  only  change 
possible  is  that  to  a  region  of  less  efficacy.  Consequently,  the 
equation  is  that  of  the  boundary  of  the  best  form  of  cross-section. 
The  curve  is  symmetrical  about  the  maximum  radius  vector,  the 

value  of  which  is  —7=. 

Vev 

Similarly,  to  arrange  a  given  number  of  turns  to  give  the  maxi- 
mum value  of  G,  their  traces  must  be  included  within  the  curve, 

r  =  (— )  sin2  a.     The  gain  from  using  the  best  form  of  cross- 

\  6c  ' 

section  is  small. 

Graded  Coils. — As  the  inner  turns  of  the  coil  of  a  Thomson 
galvanometer  are  very  near  the  needle  they  are  much  more  effect- 
ive than  those  in  the  outer  portion  of  the  coil,  which,  while  they 
add  much  to  the  resistance  of  the  instrument,  contribute  com- 
paratively little  to  the  galvanometer  constant.  This  suggests 
that  with  a  coil  of  a  definite  resistance,  it  might  be  best  to  con- 
centrate the  resistance  in  the  turns  near  the  needle,  winding  this 
part  of  the  coil  with  a  finer  wire  than  that  used  for  the  outer 
portion.  Maxwell  has  shown  in  his  "  Treatise  on  Electricity  and 
Magnetism,"  *  Art.  719,  that  the  diameter  of  the  wire  should 
increase  with  the  diameter  of  the  layer  of  which  it  forms  a  part, 
the  exact  law  depending  on  the  relation  between  the  diameters 
of  the  covered  and  the  bare  wire. 

As  it  is  not  possible  to  wind  the  coil  with  a  wire  having  a  cross- 
section  which  is  a  function  of  its  distance  from  the  end  of  the 
wire,  it  is  customary  to  wind  the  coil  in  three  or  four  sections,  each 
of  a  single  size  of  wire. 

In  a  very  sensitive  galvanometer  having  a  resistance  of  25 
ohms,  the  three  sections  were  wound  with  No.  40,  No.  34  and 
No.  26  B.  &  S.  gage.  The  thickness  of  the  insulation  was  0.002 
cm.  The  galvanometer  constant  with  the  instrument  so  wound 
was  about  33  per  cent,  greater  than  if  a  No.  26  wire  had  been 

*  Third  edition. 


16  ELECTRICAL  MEASUREMENTS 

used  for  the  entire  coil,  this  being  the  size  which  would  be  most 
advantageous  if  the  coil  were  uniformly  wound.* 

Relation  between  the  Galvanometer  Constant  and  the  Resist- 
ance of  a  Thomson  Galvanometer.  —  The  magnetic  effects  ob- 
tained by  using  coils  having  the  same  dimensions  but  wound 
with  wires  of  different  sizes  are  proportional  to  the  ampere-turns; 
the  galvanometer  constant,  G,  is  therefore  proportional  to  the 
total  number  of  turns  in  the  coil.  Let  A  be  the  area  of  the  cross- 
section  of  the  coil,  and  n'  the  number  of  turns  which  thread 
through  a  square  centimeter  of  the  cross-section.  Suppose  first 
that  the  thickness  of  the  insulation  is  zero  and  that  the  diameter 
of  the  wire  is  B\.  Then 

G  =  kAn'  =  Kri  =  ~ 


-I 

where  k  and  K  are  constants. 

The  resistance  per  unit  volume  of  the  coil,  w,  will  be 

•Km'      Ki 
w:    -B?   -BS 

and  the  galvanometer  resistance,  if  V  is  the  volume  of  the  coil, 
will  be 


/.  G  =  K,RG  (2) 

So  if  the  thickness  of  the  insulation  is  zero,  the  galvanometer 
constant  is  proportional  to  the  square  root  of  the  galvanometer 
resistance. 

Suppose  the  bobbin  to  be  filled  with  an  insulated  wire,  the 
diameter  outside  of  the  insulation,  designated  by  C,  being  the 
same  as  that  of  the  bare  wire  just  considered.  Let  the  diameter 
of  the  wire  itself  be  B.  As  the  number  of  turns  has  remained 
the  same,  G  is  not  changed  but  the  resistance  will  be  increased 

C2 
in  the  ratio  ~2;  call  this  ratio  y2,  then  to  keep  G  the  same  if  the 

new  value  of  RG  be  used, 


G  =  K,         2-  (3) 

£/ 

*  The  construction  of  a  graded  coil  of  a  definite  resistance  and  having 
three  sections  is  discussed  by  C.  G.  ABBOT  in  the  Annals  of  the  Astrophy- 
sical  Observatory,  vol.  1,  1900,  p.  244,  where  all  the  necessary  formulae  are 
given. 


THE  MEASUREMENT  OF  CURRENT  17 

or,  if  the  ratio  of  the  area  of  the  bare  to  that  of  the  covered  wire 
be  u, 

G  =  KsVuR^  (4) 

The  Best  Resistance  for  a  Thomson  Galvanometer. — It  is  well 
known  that  in  the  practice  of  most  methods  of  electrical  testing, 
the  precision  obtainable  depends  on  the  proper  adjustment  of  the 
galvanometer  resistance  to  the  work  in  hand. 

Consider  the  simple  case  of  a  galvanometer  in  series  with  a 
definite  resistance,  R,  and  a  battery  of  electromotive  force  E. 
It  will  be  assumed  that  the  bobbin  on  which  the  galvanometer 
coil  is  wound  is  of  fixed  dimensions. 

It  is  easy  to  see  that  if  a  very  large  wire  is  used  the  current 
will  be  considerable,  on  account  of  the.  low  resistance,  but  as 
there  are  only  a  few  turns,  the  ampere-turns  or  the  magnetic 
effect  at  the  needle,  to  which  the  deflection  is  proportional,  will 
be  small.  If  a  very  fine  wire  is  used,  the  resistance  will  be  large 
and  the  current  small  and  while  the  number  of  turns  is  great,  the 
ampere-turns  and  the  resulting  deflection  will  again  be  small. 
Between  these  two  extremes  there  will  be  a  size  of  wire  which 
will  correspond  to  a  maximum  deflection  of  the  galvanometer. 

The  "best  galvanometer  resistance"  is  that  obtained  when  the 
coil  is  wound  with  the  size  of  wire  which  renders  the  deflection 
a  maximum. 

The  deflection  of  the  instrument,  D,  will  be  proportional  to  the 
magnetic  force  at  the  needle,  or 

D  =  K1GG  / 

and 

E 


R  +  RG 

.   D  =  K'E^/uRy 
R  -\-  Ro 

R  is  the  resistance  external  to  the  galvanometer.  It  is  to  be 
noticed  that  RG  is  a  function  of  u.  The  deflection  is  to  be  made 
a  maximum  by  varying  RG .  If  V  is  the  fixed  volume  of  the  coil 
and  w  is  the  resistance  per  unit  volume  of  the  winding, 

Ra  =  Vw 


18 


ELECTRICAL  MEASUREMENTS 


and 


D  = 


(5) 


R  +  Vw 

The  value  of  D  is  to  be  made  a  maximum  by  properly  choosing  the 
size  of  wire.  In  order  that  this  may  be  done  data  must  be  at 
hand  concerning  the  resistance  per  unit  volume  of  various  sizes 
of  the  insulated  wire,  as  well  as  the  relation  of  the  thickness  of 
the  insulation  to  the  diameter  of  the  conductor.  In  the  pre- 
liminary discussion  of  methods  of  measurement  it  is  sufficient 
to  assume  that  G  =  K\/RG ,  in  which  case  the  maximum  deflection 
is  obtained  when 

RG  =  R 

that  is,  when  the  galvanometer  resistance  is  equal  to  that  of  the 
remainder  of  the  circuit.  If  the  galvanometer  constant  be 
taken  as 

G  =  K(RG)n 


the  deflection  will  be  a  maximum  when 


(6) 


Some  authorities  recommend  that  n  be  taken  as  %  instead  of  J^ 
as  just  used. 

A  table  of  rough  data  concerning  a  particular  make  of  double 
silk-covered  wire  is  given  below. 

TABLE  OP  ROUGH  DATA  ON  D.S.C.  Cu.  WIRE 


B.  AS. 
gage  No. 

w  =»  ohms 
per  cu.  in. 

y 

u 

Lb.  per 
cu.  in. 

B.  AS. 
gage  No. 

20 

0.76 

1.12 

0.79 

0.24 

20 

22 

2.0 

1.20 

0.69 

0.23 

22~ 

24 

5.0 

.27 

0.62 

0.21 

24 

26 

12.0 

.35 

0.55 

0.19 

26 

28 

25.0 

.43 

0.49 

0.17 

28 

30 

54.0 

.52 

0.43 

0.14 

30 

32 

105.0 

.64 

0.37 

0.12 

32 

34 

195.0 

.79 

0.31 

0.08 

34 

36 

355.0 

2.00 

0.25 

0.075 

36 

38 

630.0 

2.29 

0.19 

0.06 

38 

40 

1050.0 

2.77 

0.13 

0.05 

40 

THE  MEASUREMENT  OF  CURRENT 


19 


To  illustrate  the  influence  of  the  size  of  wire  on  the  deflection 
of  a  galvanometer  suppose  the  volume  of  the  coil  to  be  5  cu.  in. 
and  the  external  resistance  1,900  ohms.  The  relative  deflections 
calculated  by  aid  of  formula  (5)  and  the  table  are  plotted  in 
Fig.  9. 

The  figure  shows  that  it  is  better  to  err  on  the  side  of  too  great 
resistance  and  that  a  considerable  departure  from  the  ideal 


No  32 


p 


pNo.30 


10 


No.34 


No.36 


External  Resi 


tance-1900  Ohms 


No.40 


NT™ 


0  1000         2000         3000         4000        5000        6000 

Galvanometer  Resistance-  Ohms 
FIG.  9. — Illustrating  effect  of  galvanometer  resistance  on  the  deflection. 

resistance  does  not  greatly  affect  the  sensitiveness  of  the 
arrangement. 

An  important  use  of  the  reflecting  galvanometer  is  in  insula- 
tion testing,  where  the  current  is  measured  in  a  circuit  of  exceed- 
ingly high  resistance.  The  galvanometer  resistance  cannot  be 
more  than  a  few  thousand  ohms  so  the  current  is  practically 
independent  of  it.  This  case  corresponds  to  that  of  the  ordinary 
ammeter;  every  turn  adds  something  to  the  deflection,  the 
amount  becoming  smaller  and  smaller  as  the  diameter  of  the  coils 
increases.  In  this  case,  there  is  no  "best  resistance." 

The  Sensitiveness  of  Reflecting  Galvanometers. — The  sensi- 
tiveness of  a  Thomson  galvanometer  depends  on  the  arrangement 


20  ELECTRICAL  MEASUREMENTS 

and  winding  of  the  coils,  on  the  construction  of  the  suspended 
magnetic  system,  on  the  strength  and  position  of  the  neutralizing 
magnets  which  produce  the  controlling  field,  on  the  torsional 
constant  of  the  suspension  fiber,  and  on  its  initial  torsion.  This 
last  must  be  removed  when  the  galvanometer  is  set  up,  as  its 
presence  necessitates  a  strong  controlling  field  to  bring  the 
needle  to  its  zero  position. 

Ampere  Sensitivity.  Microampere  Sensitivity.  —  Quantita- 
tively, the  current  sensitivity  of  a  galvanometer  is  the  deflection, 
as  read  from  the  scale,  per  unit  current.  This  simple  statement  is 
not  sufficiently  definite,  so  in  order  to  obtain  results  that  admit  of 
comparisons  being  made  between  different  instruments,  some  con- 
vention must  be  adopted  as  to  the  conditions  under  which  the 
sensitivity  is  to  be  measured. 

It  will  be  assumed  that  one  of  the  mirror  and  scale  methods  of 
reading  is  used.  The  current,  IG,  will  be  stated  in  amperes,  the 
scale  deflection  D,  in  millimeters,  and  the  scale  distance  L,  in 

D 

meters  (1,000  scale  divisions).     Then,  Sz  =  YJ~  *s  the  deflection 

LjlG 

in  millimeters  which  would  be  produced  by  unit  current  if  the 
scale  had  been  at  a  meter's  distance.  Sr  will  be  a  very  large 
number;  consequently,  for  convenience  in  writing,  the  micro- 
ampere (10~6  ampere)  is  frequently  used  as  the  unit  of  current. 
This  gives  the  microampere  sensitivity. 

Relation  between  Time  of  Vibration  and  Current  Sensitivity.— 
By  common  consent  the  sensitivity  is  measured  when  the  sus- 
pended system  has  a  stated  time  of  vibration. 

The  connection  of  the  sensitivity  with  the  time  of  vibration  of 
the  needle  system  will  be  seen  from  the  following.  If  the  damp- 
ing due  to  air  friction  be  neglected,  the  time  of  vibration,  T0  of 
a  suspended  magnetic  system,  having  a  moment  of  intertia  P, 
and  a  magnetic  moment  M,  when  placed  in  a  field  of  strength  H, 
will  be 


The  current  through  the  instrument  is  given  nearly  enough  by 


z> 

LG  ~      G     2000L 


THE  MEASUREMENT  OF  CURRENT  21 

The  deflection  is 


n 

~H 


D^       200G  _  2  _  «0 

'  '  **<  ~  IGL  ~      H  P  ~P~ 

Therefore,  with  any  given  magnetic  system,  the  sensitivity  is 
proportional  to  the  square  of  the  time  of  vibration.  If  this  be 
doubled  by  changing  H,  the  sensitivity  will  be  increased  fourfold, 
for  to  double  the  time  of  vibration  the  directive  force  must  be 
reduced  to  one-fourth  of  its  previous  value,  so  the  deflection  due 
to  the  same  value  of  the  current  is  quadrupled. 

If  the  needle  system  is  very  light  the  damping  due  to  air  fric- 
tion will  be  so  great  that  there  will  be  a  considerable  departure 
from  the  above  relation.  The  sensitivity  of  modern  research 
galvanometers  with  very  delicate  suspended  systems  is  more 
nearly  proportional  to  the  first  than  to  the  second  power  of  the 
time  of  swing.  Instruments  with  exceedingly  light  systems  are 
sometimes  operated  in  vacuo. 

In  comparing  instruments,  the  sensitivity  must  be  reduced 
to  the  value  it  would  have  if  the  movable  system  had  some  definite 
time  of  vibration;  10  sec.  for  a  complete  swing  is  that  commonly 
taken. 

Normal  Sensitivity.  —  It  is  unfair  to  compare  instruments  which 
have  very  different  resistances  and  different  times  of  vibration. 
It  is  desirable  to  reduce  the  sensitivities  to  the  values  they  would 
have  with  the  galvanometers  wound  to  a  standard  resistance,  1 
ohm,  with  a  wire  having  an  insulation  of  zero  thickness,  and 
with  a  needle  system  whose  time  of  vibration  is  10  sec.  From  the 
previous  discussion  the  normal  current  sensitivity  is 

D    10*  _y^ 
-  * 


Volt  Sensitivity.  Microvolt  Sensitivity.  —  The  volt  sensitivity 
under  any  given  conditions  is  the  deflection  per  unit  voltage  and 
is  consequently  the  current  sensitivity  divided  by  the  resistance. 
When  dealing  with  moving  coil  galvanometers  (page  38)  the 
condition  is  frequently  imposed  that  the  resistance  of  the  circuit 
shall  be  such  that  the  galvanometer  is  critically  damped. 


22 


ELECTRICAL  MEASUREMENTS 


Megohm  Sensitivity. — The  megohm  sensitivity  is  the  number 
of  megohms  which  must  be  inserted  in  a  circuit  containing  an 
e.m.f.  of  1  volt  in  order  to  obtain  a  galvanometer  deflection  of 
1  mm.,  at  a  meter's  scale  distance.  This  is  the  same,  numerically, 
as  the  microampere  sensitivity,  referred  to  on  page  20. 

Design  for  a  Reflecting  Galvanometer.5 — A  modern  design 
for  a  reflecting  galvanometer  with  magnetic  shielding  is  shown 
in  Fig.  10. 


i 


:    FIG.  10. — Shielded  Thomson  galvanometer. 


The  support  for  the  coils  and  the  suspended  system  is  shown 
at  the  left  hand  of  the  figure.  It  consists  of  a  brass  rod,  3.8  cm. 
in  diameter.  This  is  divided  longitudinally  along  the  axis  and 
the  two  parts  are  hinged  together  at  de.  A  groove  mn  is  milled 
lengthwise  in  both  halves  and  serves  to  accommodate  the  sus- 
pended system.  When  the  instrument  is  ready  for  use,  the 
space  between  the  coils  is  about  2J^  mm.,  just  sufficient  to  allow 
the  needle  system  to  turn  around.  There  are  small  holes  along 
the  axis  of  the  coils,  denoted  by  I  and  transverse  saw  cuts  in 
the  uprights,  denoted  by  s;  by  this  means  the  needle  system  can 
be  observed  when  the  coils  are  in  their  proper  position. 


THE  MEASUREMENT  OF  CURRENT 


23 


N 


N 


N      S 


N 


The  window,  k,  allows  the  mirror  to  be  observed,  the  hard 
rubber  base,  B\,  upon  which  the  shields  rest  being  cut  away  for 
that  purpose,  as  shown  in  the  cross-section. 

The  needle  system  is  suspended  by  a  quartz  fiber,  which  is 
mounted  on  a  swinging  support  at  p,  by  which  the  system  may  be 
centered.  When  the  coil  support  is  opened,  the  needle  system 
may  be  swung  forward  for  examination. 

The  arched  piece  L  carries  the  control  magnet  M ,  which  is 
made  of  bent  clock  spring.  By  it,  the  zero  point  and  the  sen- 
sitiveness of  the  galvanometer  may  be  changed. 
The  needle  system  is  not  adjusted  for  astaticism. 

The  coils  are  wound  in  three  sections,  the  inner 
consisting  of  81  cm.  of  No.  38  wire,  the  middle 
section  of  328  cm.  of  No.  32  wire  and  'the  outer 
section  of  1,318  cm.  of  No.  26  wire.  Each  of  the 
finished  coils  has  a  resistance  of  5.6  ohms. 

To  guard  against  the  effects  of  static  charges, 
the  plane  faces  of  the  coils  are  covered  with  tin 
foil.  The  terminal  wires  of  each  coil  are  twisted 
together  and  carried  down  through  channels  in 
the  upright  and  each  coil  has  its  own  set  of  ter- 
minals. 

The  coils  are  mounted  in  the  support  by  means 
of  an  insulating  wax.  The  shields  are  those  re- 
ferred to  on  page  9. 

The  sensitivity  attained  with  all  the  coils  in  parallel  is  3  X  109, 
the  time  of  a  complete  swing  being  6  seconds. 

The  Broca  Galvanometer.6 — Various  experimenters  have 
suggested  the  use  of  a  needle  system  consisting  of  two  slender 
vertical  magnets  as  shown  at  A  in  Fig.  11. 

In  this  case  two  pairs  of  coils  would  be  used,  acting  respectively 
on  the  upper  and  lower  pair  of  poles.  Practically,  it  is  very  diffi- 
cult, if  not  impossible,  to  astaticize  such  a  system,  for  the  magnets 
must  be  exactly  parallel  to  the  axis  of  rotation. 

In  the  Broca  instrument  the  vertical  needles  are  magnetized 
with  consequent  poles  at  the  middle  of  their  lengths  as  shown  at 
B  in  Fig.  11.  Hence  it  is  easy  to  astaticize  the  system  by  re- 
touching the  magnets,  and  this  is  its  advantage. 


N 


A  B 

FIG.  11.— 
Movable  sys- 
tem with  ver- 
tical needles. 


24 


ELECTRICAL  MEASUREMENTS 


In  the  instrument  shown  in  Fig.  12,  a  single  pair  of  coils  acting 
principally  on  the  consequent  poles  is  used. 

The  control  magnet  is  at  B.  By  it  the  time  of  vibration  may  be 
varied  from  about  5  to  20  seconds.  A  clamping  device  by  which  the 
needle  may  be  held  in  place  is  actuated  by  the  knob  D.  Damping 
is  accomplished  by  a  light  aluminum  vane  G  which  swings  be- 
tween two  adjustable  plates,  manipulated  by  the  knobs  C.  A 
quartz  fiber  suspension  is  used. 

The  coils  are  so  mounted  that  they  are  readily  changed  and  the 
instrument  thus  adapted  to  different  pieces  of  work. 


FIG.  12. — Broca  galvanometer. 

THE    MOTION  OF  THE  SUSPENDED  SYSTEM  OF  A 
GALVANOMETER 

Suppose  that  when  the  movable  system  of  a  galvanometer  is  at 
rest,  the  circuit  is  suddenly  closed  so  that  a  current  flows  through 
the  instrument.  Experience  shows  that  in  some  cases  the  mov- 
able system  arrives  at  its  final  deflected  position  by  a  series  of 
oscillations  of  diminishing  amplitude,  in  other  cases  by  a  steady 
increase  of  the  deflection  without  oscillations. 

It  is  desirable  to  derive  the  equations  which  will  represent  the 
motion  of  the  system  sufficiently  well  for  practical  purposes,  for 
the  general  considerations  thus  introduced  are  of  importance  in 


THE  MEASUREMENT  OF  CURRENT  25 

dealing  with  both  current  and  ballistic  galvanometers.  An  im- 
portant special  case  is  that  of  the  critically  damped  instrument  of 
the  D'Arsonval  type,  as  ordinarily  used,  and  also  when  the 
period  has  been  so  reduced  that  the  instrument  has  become  an 
oscillograph  capable  of  following  a  complex  wave  in  its  variations. 
The  Equation  of  Motion.  —  1.  The  angular  deflection  of  a 
reflecting  galvanometer  is  always  small  so  the  deflecting  moment 
at  any  instant  may  be  taken  as  proportional  to  the  instantaneous 
value  of  the  current  and  represented  by  Ci  where  C  is  a  constant 
depending  on  the  construction  of  the  instrument. 

2.  For  small  deflections  the  restoring  moment  will  be  pro- 
portional to  the  angle  through  which  the  system  has  been  turned, 
that  is,  it  will  be  equal  to  rd  where  6  is  the  angle  of  deflection  and 
T  is  the  restoring  moment  for  unit  angular  deflection. 

3.  The  system  as  it  moves  is  retarded  by  air  friction,  etc.,  and 
in  some  cases  by  induced  currents.     It  is  customary  to  assume 
that  this  retarding  moment  is  proportional  to  the  angular  velocity 

of  the  system,  and  is  therefore  represented  by  k  _^  where  k  is  the 

coefficient  of  damping.* 

Let  P  be  the  moment  of  inertia  of  the  movable  system.  The 
total  moment  acting  to  change  the  angular  velocity  of  a  body 
rotating  about  a  fixed  axis  is  the  product  of  the  moment  of  inertia 
and  the  angular  acceleration.  On  equating  this  product  to  the 
sum  of  the  turning  moments  acting  on  the  system 

pM-a     re      kde- 
p  W  '  '  k  dt 

Consequently,  the  motion  takes  place  according  to  the  equation 


*  This  law  of  damping  was  introduced  by  GAUSS  and  W.  WEBER  in  their 
study  of  the  behavior  of  the  vibrating  magnets  used  in  their  magnetic 
measurements  at  Gottingen,  1836-37.  With  air  damping,  in  order  that  this 
law  be  reasonably  well  fulfilled,  the  damping  must  be  slight,  the  amplitude 
of  the  vibration  small  and  the  restoring  moment  due  to  the  suspension 
large.  That  this  law  is  not  absolutely  exact  is  apparent,  for,  acqording  to 
it,  the  movable  system  when  once  set  in  vibration  would  continue  to  swing 
for  an  infinite  time  with  a  constantly  decreasing  amplitude.  But  it  is  a 
matter  of  common  experience  that  the  system  comes  to  rest  in  a  compara- 
tively short  time.  However,  the  results  obtained  by  GAUSS'S  theory  are 
in  close  enough  agreement  with  the  observed  facts  to  warrant  its  use. 


26  ELECTRICAL  MEASUREMENTS 

The  right-hand  member  of  equation  (9)  may  be  a  function  of 
t,  constant,  or  zero  according  to  the  conditions  of  the  problem. 
In  this  section  i  will  be  taken  as  constant  (circuit  closed)  or  zero 
(circuit  opened). 

The  mathematical  form  of  equation  (9)  and  the  following  dis- 
cussion should  be  compared  with  that  for  the  displacement  of 
electricity  in  a  circuit  containing  resistance,  inductance,  and 
capacity  in  series. 

The  deflection  of  a  galvanometer  may  be  oscillatory  or  non- 
oscillatory  and  its  ultimate  value  will  be  most  quickly  attained 
if.  the  conditions  are  such  that  the  motion  is  just  becoming  non- 

k2 
oscillatory.     This  occurs  when  the  relation  —  =  4P  is  on  the 

point  of  being  fulfilled.     The  instrument  is  then  said  to  be 
critically  damped. 

k2 
When  —  >  4P  the  motion  of  the  suspended  system  will  be  non- 

k2 
oscillatory  and  when  —  <  4P  it  will  be  oscillatory.     When  the 

instrument  is  not  critically  damped  the  solution  of  (9)  is* 


^  -  «-/—•*«] 


and  W2  are  the  roots  of  the  equation 

Pra2  -f  km  +  T  =  0 


or 


k     .       k2        T 
2P +VIP*  -  P 


k  k2        T  ,10x 

-  2P  -  VS*  -  P 


The  constants  C\  and  Cz  must  be  determined  to  fit  the  condi- 
tions of  the  particular  case  under  consideration.  When  a  current 
of  a  definite  strength  is  sent  through  the  galvanometer 

i  =  I,  a  constant. 

*See  COHEN'S  "Differential  Equations,"  p.  105;  CAMPBELL'S  "Diffe- 
ential  Equations,"  p.  56. 


THE  MEASUREMENT  OF  CURRENT  27 

At  t  =  0  both  the  deflection  and  the  angular  velocity  are  zero,  or 

t  =  o        e  =  o 


Imposing  the  first  of  these  conditions  on  (10)  gives 

CT 

0  =  Ci  +  C2  +  ^ 

CI 

but  -  -  «  0FJ  the  final  value  of  the  deflection. 

=  Ciwi  +  C2w2  =  0 


6Fmz  BFml 

,  and  62  = 


.  .  , 

m2  —  mi  m2  —  mi 

The  value  of  6  which  fulfils  the  conditions  is  therefore 

(is) 

—  mi 

If,  when  the  needle  is  at  rest  in  its  deflected  position,  the  cir- 
cuit is  broken,  the  deflecting  moment  due  to  the  current  becomes 
zero,  so 


When 

t  =  0         6  =  BF 
and 

•-»  s-o 

.'.  «,  =  Ci  +  C2 
and 

miCi  +  m-2.Cz  =  0. 
Therefore 


Non-oscillatory  Deflection.  —  If  fc2  >  4rP,  both  mi  and  m2  are 
real  and  negative  and  (13)  is  the  equation  of  a  curve  which 
gradually  rises  toward  the  value  0F  ;  in  this  case,  the  galva- 


28 


ELECTRICAL  MEASUREMENTS 


nometer  is  said  to  be  over-damped.  When  the  circuit  is  broken, 
the  needle  returns  to  zero  according  to  equation  (15).  Equations 
(13)  and  (15)  are  plotted  in  Fig.  13  where  the  values  r  =  0.2, 
P  =  0.2  and  k  =  1.0  are  assumed. 


01     234     5     6     7     8     9    10    11    12   13    14   15    16   17    18  19 
Time  in  Seconds 


01234     56     7     8     9    10    11   12   13   14   15   16    17    18  19  20 
Time  in  Seconds 

FIG.  13. — Illustrating  the  motion  of  galvanometer  needle. 

Oscillatory  Deflection. — When  fc2  <  4rP,  mi  and  ra2  are  com- 
plex, that  is 

mi  =  —  a  +  jb 
w2  =  —  a  —  jb 


THE  MEASUREMENT  OF  CURRENT  29 

where 

k         .  ,  IT W 

a  =  ^p  and  b  =-  ^-  -  — • 

In  this  case,  the  final  deflection  is  attained  by  a  series  of 
oscillations.  If  the  values  of  mi  and  ra2  are  substituted  in  (10) 
and  the  resulting  equation  simplified  by  the  use  of  the  exponential 
values  of  the  sine  and  cosine  and  the  relation 

A  sin  0  +  B  cos  0  =  A/A2  +  B2  sin  (0  +  tan"1  -. 
it  will  be  found  that 

\  Till 

(16) 

The  variable  part  of  (16)  represents  an  oscillation  of  con- 
stantly decreasing  magnitude  and  having  a  period, 

9^-  9^- 

(17) 


6  =  B    -  e*-at  sin     bt  +  tan-1 


P       4P2 
The  time  of  a  complete  swing  when  no  damping  is  present  is 


So  0  =  6F  -  BF  YQ  sin    y  t  +  tan-1  (18) 

The  elongations,   or  maximum   and   minimum    values    of    the 
deflection,  occur  when 

T  T 


If,  when  the  needle  is  at  rest  in  its  deflected  position,  the 
circuit  is  broken,  the  return  to  zero  is  by  a  series  of  oscillations 
according  to  the  equation 

(19) 

Equations  (18)  and  (19)  are  plotted  in  Fig.  13  where  the  values 
r  =  0.2,  P  =  0.2  and  k  =  0.1  are  assumed. 


30  ELECTRICAL  MEASUREMENTS 

kT 
Logarithmic  Decrement. — Let  X  =  4p,  then    (18)    and    (19) 

become 

0  =  0F  -  6F  Y  e  ~  ™*  sin  T  ^  -f  tan~ 
and 

0  =  0p7r  c  ~  ^z' "  sin  l-sr  +  tan-1  ?  I  (19a) 


The  utility  of  this  substitution  lies  in  the  fact  that  X  is  much 
more  easily  determined  than  its  components  k  and  P. 

X  is  called  the  Napierian  logarithmic  decrement;  it  is  a  quantity 
of  importance  in  the  theory  of  damped  vibrations. 

The  first  elongation  after  the  circuit  is  broken  occurs  when 

T 

t  =  —      Substituting  this  value  in  (19a)  and  using  (21)  gives 

01    =    6F  €~X  COS  7T 

T 

The  nth  elongation,  when  t  =  n^-,  is 

Zi 

Sn  =  0F  e~nx  cos  nr. 
.    ?!  =    x(n-i) 

'On 

and 


The  method  of  determining  X  is  obvious :  To  obtain  the  neces- 
sary data  one  has  only  to  set  the  movable  system  in  motion, 
read  an  elongation,  which  will  be  called  0i  and,  after  a  counted 
number  of  elongations  read  0n. 

Experiment  shows  that  with  air  damping  X  is  slightly  affected 
by  the  amplitude  of  vibration,  but  not  enough  to  give  rise  to 
practical  difficulties. 

Influence  of  Damping  on  the  Time  of  Vibration. — From  the 
above, 

T  = 

\T_  &_  /47T2    _ 

Tz 


THE  MEASUREMENT  OF  CURRENT  31 


•• 

From  this  it  is  seen  that  X  must  be  large  before  it  greatly  affects 
the  time  of  vibration. 

Critical  Damping.  —  A  galvanometer  is  critically  damped  when 
the  motion  of  the  needle  is  just  becoming  non-oscillatory. 
In  this  case,  when  the  current  /  is  constant  and  k2  =  4rP  the 
solution  of  (9)  becomes 

0  =  BF  +  6~%P  [d  +  Cd]  (22) 

To  determine  Ci  and  C2 

t  =  0  9  =  0 

1-0          J  =  0 

dt 


dd\  /to  i 

JT  I          -  -^p  H    ^  2  = 


"  2P' 

So  e  =  e         e  €-^\l        A  t\  (23) 

For  this  case  2P  =  T 

and 


»-«,-«,«    (^'(l +  «?*}•  (24) 

I.  -t  0       J 

When  the  circuit  is  broken  the  needle  returns  to  zero,  in  accord- 
ance with  the  equation 

•d  =  dFe-(^t\l  +  ~t\  (25) 

l  J-  o   i 

Fig.   13   shows  the  character  of  the  motion  in  this  case  when 
T  =  0.2  and  P  =  0.2. 

Using  the  above  equations  the  time  required  for  the  deflection 
to  approach  within  a  given  percentage  of  its  ultimate  value  may 
be  calculated.  The  results  for  a  particular  case  are  shown  in 


32 


ELECTRICAL  MEASUREMENTS 


Fig.  14;  it  is  seen  that  the  reading  is  most  quickly  obtained  when 
the  instrument  [is  very  nearly  critically  damped.  The  deflec- 
tion of  a  critically  damped  galvanometer  is  within  J/fo  per  cent, 
of  its  ultimate  value,  at  a  time  which  is  approximately  equal 
to  1.5 TV  and  within  1  per  cent,  at  a  time  which  is  approxi- 
mately equal  to  T0. 


28 


agio 


& 


.08  .10  .12  .14  .16  .18 .20  .22  .24 .26  .28  .30  .32 .34  .36  .38  .40  .42  .44  .46  .48 .50  .52 .54  .56 .58 .60 
Damping  Constant   Jc 

FIG.  14. — Showing  the  effect  of  damping  as  the  time  required  by  a  galvan- 
ometer to  attain  its  deflection. 

The  D'Arsonval  or  Moving-coil  Galvanometer.7 — Sir  William 
Thomson  used  the  suspended-coil  principle  in  his  siphon  re- 
corder (1870)  and  its  application  to  galvanometers  was  later 
suggested  by  Maxwell  in  his  Treatise  on  Electricity  and 
Magnetism. 

The  name  D'Arsonval  is  frequently  applied  to  galvanometers 
of  this  class,  attention  having  been  recalled  to  them  by  Deprez 
and  D'Arsonval  in  1882. 

The  great  practical  advantage  of  this  instrument  lies  in  its 
freedom  from  the  effects  of  stray  fields  and  the  ease  with  which  a 
long  and  uniform  scale  may  be  attained.  It  is  these  things  that 
have  caused  it  to  be  adopted,  in  a  modified  form,  for  direct- 
current  ammeters  and  voltmeters. 

The  essential  features  of  a  moving-coil  galvanometer  are 
shown  in  Fig.  15.  The  field  is  furnished  by  a  strong  permanent 
magnet  and  the  movable  coil  swings  in  the  air  gaps  between  the 
poles  of  the  magnet  and  a  fixed  iron  core.  The  coil  is  hung  by  a 
fine  wire  suspension  which  also  serves  as  a  lead,  while  below  the 


THE  MEASUREMENT  OF  CURRENT 


33 


coil  the  current  is  taken  out  by  a  loosely  coiled  metallic  spiral.  A 
proper  torsion  head  for  adjusting  the  coil  vertically  and  setting 
the  zero  reading  is  provided.  The  entire  coil  system  is  mounted 
in  a  removable  frame  so  that  the  coils  may  be  readily  changed. 
Suppose  the  coil  is  rectangular,  the  total  length  of  active  wire 
is  I  and  the  half  breadth  of  the  coil  is  b,  and  that  the  field,  H ,  in 
which  the  coil  is  placed  is  uniform.  The  turning  moment  due  to 
the  current,  7,  is 

M  =  IHlb  cos  0 


FIG.   15. — Moving-coil  galvanometer. 

where  6  is  the  angle  between  the  lines  of  force  and  the  plane  of 
the  coil.  If  the  motion  of  the  coil  be  resisted  by  a  spring,  the 
latter  will  be  twisted  until  the  restoring  moment  due  to  it  is  equal 
to  the  deflecting  moment  due  to  the  current.  If  the  zero  posi- 
tion of  the  plane  of  the  coil  is  in  the  direction  of  the  lines  of  force, 
the  restoring  moment  will  be  rB  where  r  is  the  restoring  moment 
for  unit  angular  deflection  (a  constant).  Thus,  at  equilibrium 

r6  =  IHlb  cos  0 
If  there  are  n  turns, 

7  -       T       (    e 
nHlb    \cos0 

The  D'Arsonval  galvanometer  is  a  secondary  instrument;  that 
is,  the  relation  between  the  deflection  and  the  current  is  always 


34  ELECTRICAL  MEASUREMENTS 

determined  by  calibration ;  but  the  formula  serves  to  direct  atten- 
tion to  certain  quantities  which  are  involved  in  its  action. 

The  Magnets. — It  is  seen  that  if  there  were  no  modifying  con- 
ditions the  current  sensitivity  would  increase  proportionally  to  H. 
This  indicates  that  the  magnet  should  be  very  strong.  How- 
ever, strength  is  not  the  only  thing  to  be  considered,  for  it  is  well 
known  that  so-called  permanent  magnets  gradually  lose  their 
strength,  that  is,  they  "age."  The  ageing  depends  upon  the 
quality  of  the  steel,  the  design  of  the  magnetic  circuit  and  upon 
the  temperature  variations  and  mechanical  jarring  to  which  the 
magnet  is  subjected.  Any  deterioration  will  influence  the  sensi- 
tiveness of  the  instrument,  so  in  this  and  in  many  other  cases, 
for  instance,  in  the  magnets  used  in  direct-current  ammeters  and 
voltmeters,  and  in  watt-hour  meters,  it  is  necessary  to  resort  to 
artificial  ageing.  As  pointed  out  by  Strouhal  and  Barus  this 
may  be  done  by  the  proper  heat  treatment  at  moderate  tempera- 
tures. Their  procedure  was,  after  the  magnet  had  been  hardened, 
to  heat  it  in  a  steam  bath  at  100°C.  for  20  or  30  hours,  then  magnet- 
ize it  strongly  and  afterward  heat  it  again  in  the  steam  bath  for  4 
or  5  hours.  In  addition,  some  makers  resort  to  a  partial  demag- 
netization. The  net  result  is  that  while  the  strength  of  the  mag- 
net is  reduced,  the  remaining  magnetization  is  very  permanent. 

The  temperature  coefficient  of  magnets  such  as  are  used  in 
galvanometers  and  in  direct-current  ammeters  and  voltmeters  is 
about  —0.025  per  cent,  per  degree  C.  rise  of  temperature;  it 
varies  with  the  magnet. 

Chilled  cast-iron  magnets  may  be  employed.8  In  general, 
they  are  useful  where  it  is  necessary  to  employ  forms  so  compli- 
cated that  forging  would  be  difficult. 

After  the  gray  iron  castings  have  been  machined,  they  are 
heated  to  a  bright  red  (just  under  the  melting  point)  in  a  gas 
furnace  provided  with  a  power  blast,  and  then  plunged  into  a 
cold  acid  bath  which  is  violently  stirred.  Care  must  be  taken  in 
the  manipulation  of  the  heated  castings,  for  they  are  lacking  in 
tenacity.  It  is  important  that  the  entire  mass  of  the  casting  be 
hardened;  consequently  the  heating  must  be  prolonged  until  it 
is  certain  that  the  temperature  is  practically  uniform  through- 
out the  mass. 

After  hardening,  the  magnets  are  heated  in  a  steam  bath  for  a 


THE  MEASUREMENT  OF  CURRENT 


35 


long  time  and  then  magnetized  to  saturation.  The  ageing  is 
effected  by  alternately  heating  in  steam  and  cooling  in  tap  water. 
If  the  magnets  are  magnetized  to  saturation,  the  strength  is 
reduced  about  20  per  cent,  by  this  process. 

When  properly  prepared,  chilled  cast-iron  magnets  have  a  small 
temperature  coefficient.  For  magnets  of  the  forms  used  in  instru- 
ments, the  average  decrease  of  field  strength  per  degree  rise  of  tem- 
perature, between  10°  and  100°,  is  about  0.04  per  cent.  Within 
the  ordinary  range  of  room  temperatures  it  is  much  smaller, 
about  0.013  per  cent,  per  degree. 

The  strength  of  aged  cast-iron  magnets  is  less  than  the  strength 
of  those  of  equal  weight,  made  of  special  magnet  steel. 


FIG.  16.' — Pole  pieces  for  producing  a  radial  field  and  the  resultant  field. 

Effect  of  Magnetic  Impurities  in  the  Coil. — Practically  it  is 
found  that  the  increase  in  sensitiveness  may  not  be  proportional 
to  the  increase  in  H,  for,  as  first  pointed  out  by  Ayrton  and 
Mather,  the  coil  itself  may  be  slightly  magnetic  due  to  the  pres- 
ence of  minute  amounts  of  iron  as  an  impurity  in  the  metal 
or  which  have  been  worked  into  the  insulation  during  the  process 
of  winding. 


36  ELECTRICAL  MEASUREMENTS 

Consequently,  in  very  strong  uniform  fields,  the  attraction 
between  the  magnet  and  the  induced  poles  on  the  coil,  when  it  is 
deflected  from  its  initial  position,  may  be  strong  enough  to  mate- 
rially reduce  the  sensitiveness.  In  some  cases  the  control  thus 
exercised  may  be  greater  than  that  due  to  the  suspension.  The 
magnetic  action  of  the  coil  also  gives  rise  to  indefiniteness  of  the 
zero  reading  which  will  be  displaced  in  the  direction  of  the  next 
previous  deflection.  These  difficulties  are  reduced  to  negligible 
amounts  if  a  radial  field  is  used  as  indicated  in  Fig.  16. 

Obviously,  induced  poles,  if  they  exist,  do  not  affect  the  restor- 
ing moment  when  the  coil  changes  its  position.  This  con- 
struction also  gives  a  long  and  uniform  scale.  It  was  introduced 
in  the  Weston  direct-current  ammeters  and  voltmeters  in  1888. 

When  the  coil  moves  in  a  radial  field,  the  turning  moment 
acting  upon  it  is  given  by 

M  =  IHlb. 

Suspensions. — The  materials  commonly  used  for  the  sus- 
pension wires  in  commercial  instruments  are  phosphor-bronze 
and  steel.  Silver  gives  a  low  resistance  wire  but -is  not  as  stable 
as  phosphor-bronze. 

The  sensitivity  will  be  increased  by  diminishing  the  torsion 
constant,  r,  which  is  proportional  to  the  fourth  power  of  the 
diameter  of  the  suspension  wire.  Of  course,  with  a  given  coil, 
the  stress  per  unit  area  on  the  suspension  is  inversely  as  the 
square  of  the  diameter. 

To  increase  the  sensitivity  without  increasing  the  unit  stress 
on  the  suspension,  Ayrton  and  Perry  suggested  that  a  flat  strip 
be  substituted  for  the  round  wire.  A  strip  having  a  breadth  of 
about  ten  times  its  thickness  has  approximately  one-fifth  of  the 
torsional  rigidity  of  a  round  wire  of  the  same  length  and  sectional 
area.  Such  suspensions  are  very  commonly  used  in  commercial 
moving  coil  galvanometers.  Northrup  has  suggested  the  employ- 
ment of  a  cable  of  very  fine  wires  as  a  means  of  supporting  heavy 
coils.  For  a  cable  capable  of  supporting  a  given  weight  the 
torsional  rigidity  decreases  in  proportion  as  the  number  of 
strands  is  increased.  This  form  of  suspension  is  frequently  used 
in  portable  galvanometers. 

All  connections  about  the  suspended  system  should  be  soldered, 
as  otherwise  extraneous  resistances  may  be  introduced  by  loose 


THE  MEASUREMENT  OF  CURRENT  37 

contacts  or  by  corrosion.  Rosin  should  be  used  as  a  flux,  as  it  is 
difficult  to  remove  the  last  traces  of  acid,  which  would  seriously 
corrode  the  delicate  wires.  For  the  same  reason,  so-called  non- 
corrosive  soldering  liquids  should  be  avoided. 

The  use  of  the  taut  suspension  employed  in  the  original 
D'Arsonval  instrument  is  not  advisable  unless  there  is  a  special 
provision  for  balancing  the  coil,  for  it  is  difficult  to  attach  the 
suspension  wires  so  that  their  axes  pass  through  the  center  of 
gravity  of  the  coil  when  the  suspension  is  drawn  taut.  If  this 
condition  is  not  fulfilled,  the  center  of  gravity  is  coerced  into 
taking  up  an  abnormal  position  and  the  weight  of  the  coil  will 
cause  a  turning  moment  which  will  vary  with  the  tightness  of 
the  wire  and  the  level  of  the  instrument.  For  these  reasons,  in 
sensitive  instruments  of  the  best  design,  the  coil  is  allowed  to  hang 
free  and  the  electrical  connection  at  the  bottom  of  the  coil  is 
made  by  a  loose  spiral  which  may  have  a  very  small  torsional 
rigidity.  This  procedure  also  decreases  the  stress  in  the  upper 
wire  so  that  it  may  be  made  smaller.  However,  in  special  cases 
where  the  instrument  is  to  be  subjected  to  great  changes  of  level, 
as  on  shipboard,  the  taut  wire  must  be  employed.  In  the  Sulli- 
van marine  galvanometer  and  other  similar  instruments,  the 
center  of  gravity  of  the  moving  coil  can  be  adjusted  to  its  proper 
position  by  bending  bits  of  lead  wire  which  project  from  the  coil 
frame  or  by  adjusting  two  sets  of  screws  which  project  at  right 
angles  through  and  perpendicular  to  the  shank  supporting  the 
coil. 

Effect  of  Changes  of  Temperature. — If  the  instrument  is  to  be 
used  as  an  unshunted  current  galvanometer,  a  change  of  room 
temperature  will  alter  the  calibration.  Experiments  show  that 
for  phosphor-bronze  strip  the  elasticity  decreases  about  0.05  per 
cent,  per  degree  rise  of  temperature.  The  strength  of  the  magnet 
also  diminishes  with  an  increase  of  temperature,  the  change  being 
0.01  or  0.02  per  cent,  per  degree.  It  varies  with  different  mag- 
nets. The  tendency  of  these  effects  is  toward  compensation,  but 
in  general  their  relative  magnitudes  will  not  be  such  as  to  elimi- 
nate the  error. 

If  the  instrument  is  shunted,  the  multiplying  power  of  the 
shunt  will  depend,  to  a  certain  extent,  upon  temperature  con- 
ditions, for  the  galvanometer  is  wound  with  copper  and  the 


38  ELECTRICAL  MEASUREMENTS 

shunt  is  most  probably  of  a  material  having  zero  temperature 
coefficient. 

When  the  D' Arson val  galvanometer  is  used  as  a  potential  gal- 
vanometer or  a  millivoltmeter,  there  is  an  additional  source  OT 
variation  due  to  the  change  of  resistance.  If  the  necessary  series 
resistance  is  made  partly  of  copper  and  partly  of  manganin  in 
the  proper  proportion,  its  net  temperature  coefficient  may  be 
made  such  that  the  instrument  is  almost  exactly  compensated 
for  variations  of  room  temperature. 

It  should  be  remembered  that  when  the  temperature  varies 
very  rapidly,  there  will  be  a  time  lag  in  the  change  of  resistance 
and  in  the  change  of  the  strength  of  the  magnet. 

Magnetic  Damping. — To  prevent  loss  of  time  when  using  any 
galvanometer,  it  is  necessary  that  it  be  properly  damped.  In 
the*  D'Arsonval  instrument  the  damping  may  be  attained  by 
use  of  closed  loops  of  wire  attached  to  the  movable  coil  or 
by  winding  the  coil  on  a  very  light  metal  bobbin,  as  is  done 
in  direct-current  ammeters  and  voltmeters.  The  current  in- 
duced in  the  closed  circuit  as  the  coil  swings  through  the 
magnetic  field  promptly  brings  the  coil  to  rest.  Similarly  a 
moving  coil  galvanometer,  as  will  be  seen  below,  will  be  appreci- 
ably damped  if  it  is  used  in  a  closed  circuit  of  moderate  resist- 
ance and  it  is  frequently  possible,  by  adjusting  the  resistance 
of  the  circuit  and  the  constants  of  the  galvanometer,  to  attain 
critical  damping. 

When  it  is  necessary  that  the  coil  be  perfectly  free  to  move 
from  and  be  brought  back  quickly  to  its  zero  position,  a  short 
circuiting  key,  which  must  be  free  from  thermo-electromotive 
forces,  may  be  placed  across  the  terminals  of  the  galvanometer. 
The  motion  of  the  coil  is  promptly  checked  by  depressing  the  key. 

The  damped  D'Arsonval  instrument  is  very  useful  as  a  ballistic 
galvanometer  on  account  of  its  quick  return  to  the  zero  reading. 

The  Critically  Damped  Moving-coil  Galvanometer.7— The 
field  in  which  the  coil  moves  will  be  assumed  to  be  radial. 

SYMBOLS  USED  IN  THE  DISCUSSION 

H  =  strength  of  field. 

I  =  total  length  of  active  wire. 
.  6  =  one-half  the  breadth  of  movable  coil. 


THE  MEASUREMENT  OF  CURRENT  39 

v  =  total  length  of  vertical  wire. 

h  =  total  length  of  horizontal  wire,  across  ends  of  coil, 
ra  =  mass  per  unit  length  of  bare  wire. 
m'  =  mass  per  unit  length  of  covered  wire. 

ra' 

n  = 

ra 

a  =  area  of  bare  wire. 

p  =  resistivity  of  copper,  1. 724  microhms  centimeter  at  20°C. 
8  =  density  of  copper,  8.89. 

P  =  moment  of  inertia  of  entire  moving  system. 
P'  =  moment  of  inertia  of  coil  fittings. 
T  =  torsion  constant  of  suspension,  restoring  moment  for    unit  angular 

deflection. 

6  —  deflection  at  any  instant. 
OF  =  final  value  of  6  when  a  constant  current  IF  flows  in  coil,  or  initial 

value  of  0  when  circuit  is  broken. 
i  =  current  in  coil  at  any  instant. 
IF  =  final  value  of  current  after  coil  has  come  to  rest  in  its  deflected 

position. 

To  =  time  of  an  undamped  vibration  of  movable  system. 
R  =  total  resistance  of  circuit,  including  galvanometer. 
L  =  total  inductance  of  circuit. 
RG  =  resistance  of  coil  of  galvanometer. 

E  =  e.m.f.  of  battery. 

EB  =  back  e.m.f.  generated  by  movement  of  coil. 

C  =  Hlb,  turning  moment  which  acts  on  coil  when  it  carries  unit  current. 
Si  =  current  sensitivity. 

Q 

SF  =  p-  =  voltage  sensitivity. 

\  \ 

The  turning  moment  acting  on  the  coil  at  any  instant  is  iHlb 
=  iCj  while  the  restoring  moment  is  rO.  After  the  coil  has  come 
to  rest 

T0,  =  IF€ 
or 

^    /,  =  5=  (28) 

An  important  use  of  the  moving-coil  instrument  is  in  a  closed 
circuit  of  moderate  resistance  as  occurs  with  the  Dieselhorst  or 
the  Brooks  potentiometer  or  when  the  instrument  is  used  in 
connection  with  thermo-electric  junctions.  In  these  cases  the 
resistance  of  the  circuit  is  constant  or  nearly  so. 

Consider  the  instrument  to  form  a  part  of  a  galvanic  circuit 
which  includes  a  source  of  e.m.f.  and  a  resistance  external  to  the 


40  ELECTRICAL  MEASUREMENTS 

galvanometer.  When  the  circuit  is  closed  the  coil  will  begin  to 
move  and  as  it  swings  in  the  field,  H,  a  back  e.m.f.  will  be  set  up; 
its  magnitude  will  be 

<#_„ 

dt 


EB  =Hlb^  =  C~ 


Consequently  the  current  at  any  instant  will  be 

di  M 


Let  k  be  the  damping  coefficient  when  the  galvanometer  circuit 
is  open.  This  damping  may  be  due  to  currents  induced  in  damp- 
ing loops  attached  to  the  movable  coil  or  in  a  metal  frame  upon 
which  the  coil  is  wound  and,  to  a  slight  extent,  to  the  air  damping. 
From  the  above 


or 


The  term  containing  -yr  is  negligible  so 
dt 


/C2          \ 
Here   (-~    +  kj  is  the  damping  constant  and  replaces  k  in  the 

equation  on  page  25. 

The  case  of  special  importance  is  when  the  constants  of  the 
circuit  are  such  that  the  instrument  is  critically  damped.  Then 
if  it  is  assumed  that  the  damping  is  entirely  due  to  actions  in  the 
movable  coil  itself, 


(30) 
Introducing  TQ  and  eliminating  r  gives 

(V\JL   -  2-. 
\R/2P  7  T0 


THE  MEASUREMENT  OF  CURRENT  41 

Current  and  Voltage  Sensitivity. — Using  6  in  radians  and  IF 
in  absolute  units 

0F       C 


(31) 

R  is  the  resistance  of  the  circuit  necessary  for  critical  damping. 
Using  the  microampere  sensitivity  (page  20),  if  R  is  expressed 
in  ohms  and  the  reading  in  millimeters,  on  a  scale  at  a  meter's 
distance, 

(T7  p\   /ins  v  9  nnn2\  T  P  T  37? 

i  Ort\  /iu   x  ^,uuu  \  _  197^o^_n  or>£o  -a 
~~r/  \      7r(107)2      /  r  P 

-  80  •  -JP  (32) 

T   \  T 

S     _8.X10H^. 
O^   —  o       /\    IU        x>f3 

The  voltage  sensitivity  or  the  deflection  per  microvolt  applied 
to  the  circuit  is 

*Sr 


so 

r  r«     so  , 


57  =8-Xl014~-  (33) 

In  designing,  the  formulae  may  of  course  be  worked  backward  to 
find  the  values  of  P,  r,  etc.,  corresponding  to  the  conditions  of  the 
problem. 

To  illustrate  the  utility  of  (32)  and  (33),  suppose  that  an 
instrument,  already  constructed,  is  to  be  used  in  a  circuit  having 
a  fixed  resistance  and  that  the  conditions  are  such  that  it  is 
critically  damped  or  dead  beat  but  not  sufficiently  sensitive  for 
the  work  in  hand.  There  are  two  factors  which  may  be  altered 
to  increase  the  sensitivity  without  using  a  new  coil;  the  torsional 
control  r  and  the  field  strength  H.  If  the  field  strength  is 
increased,  the  ultimate  deflection  due  to  any  current  will  be 


42  ELECTRICAL  MEASUREMENTS 

increased  in  the  same  proportion  but  the  instrument  will  no 
longer  be  dead  beat;  it  will  become  sluggish  in  its  action  so  that 
the  time  which  must  elapse  before  the  reading  can  be  taken  is  un- 
duly increased.  If  r  is  decreased  the  same  is  true,  so  two  changes 
are  necessary  if  the  critical  damping  is  to  be  preserved. 

Suppose  the  restoring  moment  of  the  spring  is  reduced  to 
one-sixteenth  of  its  original  value.  Then  by  (32)  and  (33)  both 
Si  and  Sv  will  be  increased  eightfold,  for  TV  is  increased  to  64 
times  its  former  value  and  both  Si  and  Sv  are  proportional  to 
-V/To3.  In  detail,  by  (30)  if  r  is  reduced  to  one-sixteenth  of  its 
former  value,  in  order  to  maintain  critical  damping  C  must  be 
halved.  As  the  coil  is  not  to  be  altered,  the  quantity  C  =  Hbl 
must  be  halved  by  halving  the  strength  of  field  H.  If  the  field  is 
halved  and  the  restoring  moment  reduced  to  one-sixteenth  of  its 
first  value,  the  sensitivity  will  become  eight  times  its  initial 
value. 

The  modification  will  render  the  instrument  less  prompt  in  its 
action,  for  the  time  of  an  undamped  vibration  T0  will  be  increased 
to  four  times  its  original  value. 

Expression  for  the  Field  Required  to  Produce  Critical  Damp- 

ing.7 

C*         TR0r 

W  7T/262 

Expressing  R  in  ohms 


/lO9     iTR^r       17,800  -VTRtr       112,000     IRP 
"  V  V  \  W"  ~»  "  ~W~    V  TQ 


( 


This  relation  can  be  transformed  so  that  H  is  made  to  depend  on 
the  resistance  of  the  galvanometer  coil  and  on  the  lengths  of  the 
active  and  inactive  wire. 

The  total  moment  of  inertia  of  the  moving  parts  is  (referring  to 
the  table  of  symbols) 

P  =  mn  (v  +  =)  62  +P' 

\  o/ 

p  (v  +  h)        p*  (»  -J-  h\ 

KG  =  -  ~  =  - 


a  m 

P  -P'  (P  -  P') 


mn(v -\- ^}        npb(v-\-h)  (v 

\  Of  \ 


THE  MEASUREMENT  OF  CURRENT  43 

and 

112,000 


/         JA 
npd(v  +  h)   (v  +  gj      j£p 

(P  -  P')  RG  \  To 


•"       " 


(35a) 

The  value  of  ^4  is  generally  between  600  and  800,  depending 
mainly  on  the  breadth  of  the  coil.  The  quantity  n  depends  to  a 
certain  extent  on  the  size  of  the  wire  and  will  probably  lie  between 
1.4  and  1.6. 

As  the  resistance  of  the  circuit  is  increased,  the  practical 
application  of  the  results  of  this  discussion  become  more  and  more 
difficult,  especially  if  a  quick-working  (short  period)  instrument 
is  desired. 

Auxiliary  Damping. — If  the  galvanometer  is  to  be  used  in 
circuits  of  varied  resistances,  the  damping  will  vary  to  corre- 
spond, rarely  being  such  that  the  instrument  may  be  read  quickly; 
in  such  cases  recourse  is  frequently  had  to  auxiliary  magnetic 
dampers  which  are  in  effect  closed  loops  of  wire  attached  to  the 
coil  and  swinging  in  the  same  field.  A  familiar  example  of  this  is 
the  damping  device  used  on  direct-current  ammeters  and  volt- 
meters, the  coil  being  wound  on  an  aluminum  frame  or  bobbin. 

Possible  Adjustments. — An  instrument  not  specifically  de- 
signed for  a  given  piece  of  work  may  sometimes  be  made  more 
effective  by  special  adjustment.  The  things  which  may  be 
varied  are: 

1.  The  total  resistance  of  the  circuit.     This  may  be  adjusted 
by  resistances  in  series  or.,  in  shunt  with  the  galvanometer,  as 
necessary. 

2.  The  field  strength.     This  may  be  decreased  by  using  a  mag- 
netic shunt  or  increased  by  using  a  second  set  of  magnets  in 
parallel  with  the  original  one. 

3.  The  torsion  constant  r.     The  suspension  may  be  changed. 

4.  The  damping,  by  the  use  of  an  auxiliary  damping  loop. 

5.  The   moment   of  inertia  P.     This   may   be   increased   by 
placing  weights  on  the  movable  element. 


44  ELECTRICAL  MEASUREMENTS 

/C2\ 2 
As  the  relation  ( -^ )   =  4Pr,  which  is  necessary  for  critical 

damping,  is  to  be  preserved,  two  changes  will  be  required,  the 
second  to  compensate  for  the  effect  of  the  first  on  the  damp- 
ing. 

For  example,  suppose  that  it  is  desirable  to  increase  the  total 
resistance,  R,  of  the  circuit  N  times.  If  this  is  done,  the  instru- 
ment will  become  under-damped  and  the  voltage  sensitivity 
will  be  reduced  N  times.  To  restore  the  damping  a  damping  loop 
may  be  added.  This  will  increase  To  somewhat,  due  to  the 
increased  moment  of  inertia.  As  indicated  by  the  equations, 
other  compensating  changes  are  possible. 

The  Einthoven  String  Galvanometer9. — In  this  instrument 
the  movable  element  is  either  a  very  fine  silvered  quartz  fiber 


FIG.  17. — Einthoven  string  galvanometer. 

about  8  or  10  cm.  long,  or  a  very  fine  wire.  This  is  placed  in  the 
strong  field  due  to  an  electromagnet  and  so  mounted  that  the 
tension  upon  it  may  be  varied. 

When  a  current  is  sent  through  the  fiber,  it  moves  across  the 
magnetic  field.  The  motion  is  observed  with  a  microscope  having 
a  micrometer  eyepiece,  a  magnification  of  about  100  diameters 
being  used.  The  deflections  are  proportional  to  the  current. 

Fig.  17  shows  the  essential  features  and  one  design  of  the 
complete  instrument. 


THE  MEASUREMENT  OF  CURRENT  45 

The  resistance  of  the  silvered  quartz  fiber,  which  is  used  in 
order  to  attain  a  sufficiently  light  "string,"  may  vary  between 
2,000  and  10,000  ohms;  with  a  silver  wire  about  0.02  mm.  in 
diameter,  the  resistance  is  4  or  5  ohms. 

The  electromagnet  has  a  very  massive  core  and  the  pole  pieces 
are  so  shaped  that  they  concentrate  the  field  on  the  narrow  air 
gap  in  which  the  "string"  moves.  The  magnet  is  worked  above 
saturation,  consequently  small  variations  of  the  exciting  current 
have  but  little  effect  on  the  strength  of  the  field  in  the  air  gap 
which  is  about  20,000  c.g.s.  units. 

The  time  of  swing  of  the  movable  member  of  the  Einthoven 
galvanometer  is  very  short;  it  depends  on  the  size  and  material 
of  the  "string"  and  the  tension  upon  it.  With  a  fine  silvered 
quartz  fiber  having  a  diameter  of  from  0.002  to  0.003  mm.,  and 
under  tension,  it  may  be  much  less  than  0.01  sec.,  while  with  a 
silver  wire  having  a  diameter  of  about  0.02  mm.,  it  may  approach 
0.1  sec.  when  the  tension  is  relaxed.  If  the  tension  on  the  silvered 
quartz  fiber  is  very  much  relaxed,  the  instrument  becomes 
unduly  sluggish  and  as  much  as  10  sec.  may  elapse  before  the 
deflection  is.  completed.  The  galvanometer  is  then  exceedingly 
sensitive  but  the  zero  reading  is  likely  to  be  unsteady  and  the 
fiber  may  move  out  of  focus. 

The  advantages  of  this  form  of  galvanometer  are  its  extreme 
quickness  of  action  and  immunity  from  the  effects  of  stray 
fields. 

In  a  high-resistance  circuit  the  damping  is  by  air  friction,  but 
if  the  resistance  be  low  and  shunts  are  employed  electromagnetic 
damping  is  also  present.  Einthoven  has  shown10  that  if  a  high 
resistance  instrument  is  placed  in  series  with  an  adjustable 
resistance  and  in  parallel  with  a  condenser  and  the  whole  com- 
bination shunted  around  another  resistance,  it  is  possible  to 
adjust  the  combination  so  that  the  galvanometer  is  dead  beat. 
The  instrument  thus  becomes  a  low-period  oscillograph,  suitable 
for  recording  phenomena  whose  cycle  is  completed  in  a  few 
tenths  of  a  second.* 

By  using  an  arc  lamp  and  the  proper  optical  system,  the 
deflection  may  be  projected  on  a  screen  at  about  a  meter's. dis- 

*  The  firm  of  Cans  and  Co.  manufacture  a  regosular  cillograph  (without 
damping)  based  on  the  "string"  principle. 


46 


ELECTRICAL  MEASUREMENTS 


tance.  Cyclic  phenomena  are  observed  by  the  use  of  a  revolving 
mirror,  as  is  customary.  Permanent  records  may  be  obtained 
photographically  on  a  moving  plate  or  film.  A  narrow  slit  is 
placed  immediately  in  front  of  the  photographic  surface  and 
behind  a  cylindrical  lens  so  that  the  image  of  the  fiber  appears 
on  the  sensitized  surface  as  a  shadow,  which  prevents  the  expo- 
sure of  the  part  of  the  surface  on  which  it  happens  to  fall. 
This  arrangement  is  used  in  physiological  investigations. 


^  Quartz 
Fibre 


Heater 


FIG.  18. — Duddell  thermo-galvanometer. 


The  Duddell  Thermo-galvanometer. — The  essential  features 
of  this  instrument,  which  is  based  on  the  radio-micrometer  of 
C.  Vernon  Boys,  are  indicated  in  Fig.  18. 

A  single  loop  of  silver  wire  having  a  high  conductivity  is  sus- 
pended by  a  quartz  fiber  in  the  strong  magnetic  field  due  to  a 
permanent  magnet.  At  the  lower  end  of  the  loop  there  is  a 
bismuth-antimony  thermo-couple  and  beneath  this  and  as  near 


THE  MEASUREMENT  OF  CURRENT  47 

as  possible  without  touching  it,  is  a  heater  wire  through  which 
the  current  to  be  measured  is  sent.  On  the  passage  of  the  cur- 
rent the  lower  thermal  junction  is  warmed  by  radiation  and 
convection;  consequently  a  direct  current,  due  to  the  thermo- 
electric action,  flows  around  the  loop  which  is  thus  deflected. 
The  heater  filament  is  straight  or  else  bent  back  and  forth  form- 
ing a  grid.  Its  inductance  is  therefore  very  small  and  the 
instrument  is  consequently  adapted  for  the  measurement  of 
alternating  currents  of  high  periodicity,  the  deflection,  which  is 
read  by  the  mirror  and  scale  method,  being  practically  propor- 
tional to  the  mean  square  value  of  the  current  through  the  heater. 
The  damping  is  due  to  currents  induced  in  the  loop  as  it  moves  in 
the  field  and  the  electrical  constants  are  such  that  critical  damp- 
ing is  attained.  The  period  of  the  instrument  is  3  or  4  seconds. 

As  with  any  thermo-electric  device  constancy  of  zero  reading 
depends  on  uniformity  of  temperature.  Sudden  fluctuations 
in  room  temperature  should  be  avoided.  Slow  variations  which 
give  time  for  the  temperatures  of  the  hot  and  cold  junctions  to 
equalize  are  not  nearly  as  important.  To  assist  in  maintaining 
constant  temperature  conditions,  the  working  parts  of  the  instru- 
ment are  enclosed  in  a  heavy  gun-metal  case,  the  front  of  which, 
E,  may  be  removed  when  it  is  necessary  to  inspect  or  adjust  the 
instrument.  The  zero  should  be  read  after  each  observation. 

Interchangeable  heaters  are  used.  They  are  of  various 
resistances  depending  on  the  sensitivity  required.  Those  having 
a  resistance  below  4  ohms  are  made  of  wire,  while  those  above 
this  value  consist  of  a  deposit  of  platinum  on  quartz,  made  into 
the  form  of  a  grid. 

The  sensitivity  attained,  as  given  by  the  makers  of  the  instru- 
ments, the  Cambridge  Scientific  Instrument  Co.,  is  shown  in 
the  following  table. 

The  instrument  may  be  calibrated  with  direct  currents  and 
then  used  on  alternating-current  circuits.  It  is  more  sensitive 
than  the  electrodynamometer,  not  subject  to  errors  due  to  in- 
ductance or  capacity,  and  at  high  frequencies  does  not  disturb 
the  circuit  conditions  as  much  as  the  dynamometer. 

The  sensitivity  may  be  controlled  to  a  certain  extent  by  ad- 
justing the  proximity  of  the  heater  to  the  hot  junction.  This 
is  done  by  turning  the  ebonite  milled  head,  F.  Great  care  is 


48 


ELECTRICAL  MEASUREMENTS 


necessary  in  manipulating  the  instrument  not  to  injure  the  deli- 
cate loop  or  the  thermo-couple. 


TABLE  OF  APPROXIMATE  SENSITIVITIES  OP  THERMO-GALVANOMETERS. 
DISTANCE  1,000  mm. 


SCALE 


Resistance 
of 
heater, 
ohms 

Current  to 
give  250  mm. 
deflection, 
microamperes 

Current  to 
give  10  mm. 
deflection, 
microamperes 

P.  D.  to 

give  250 
mm. 
deflection, 
millivolts 

P.  D.  to 
give  10 
mm. 
deflection, 
millivolts 

About  1,000 

110 

22 

110.0 

22.0 

About     100 
About       10 
About         4 

350 
1,100 
1,750 

70 
220 
350 

35.0 
11.0 
7.0 

7.0 
2.2 
1.4 

Heater    close    to 
junction 

About         1 

3,500 

700 

3.5 

0.7 

About         1 

10,000 

2,000 

10.0 

2.0 

\  Heater      lowered 
1  away  from  junction 

• 

The  same  principle  is  applied  in  the  Duddell  thermo-ammeter 
(see  page  60). 


POINTS  TO   BE   CONSIDERED   WHEN   SELECTING  A 
GALVANOMETER 

A  galvanometer  must  be  selected  with  special  reference  to 
the  work  to  be  done,  for  no  instrument  is  equally  useful  under  all 
sorts  of  conditions.  Among  the  points  to  be  considered  are  the 
following. 

Sensitivity. — The  sensitivity  should  be  sufficient  for  the  work 
in  hand  so  that  measurements  may  be  made  without  undue 
fatigue  and  loss  of  time.  On  the  other  hand,  a  much  higher 
sensitivity  is  not  an  advantage  for  it  means  a  more  delicate 
instrument  and  therefore  one  more  liable  to  injury  and  more 
difficult  to  manipulate.  Also,  high  sensitivity  may  mean  an  un- 
duly long  period  of  vibration  and  a  subsequent  loss  of  time  in 
making  measurements.  Sensitivity,  though  important,  should 
not  be  the  only  thing  considered  in  estimating  the  utility  of  a 
galvanometer. 

Period. — The  time  of  vibration  of  the  movable  system  should 
be  short  so  that  the  instrument  will  respond  quickly  to  the 
current. 

Damping. — When  the  instrument  is  in  use,  the  system  should, 
if  possible,  be  critically  damped.  This  will  economize  time. 


THE  MEASUREMENT  OF  CURRENT  49 

In  many  cases  the  damping  is  not  an  inherent  property  of  the 
galvanometer  but  depends  both  on  the  instrument  and  on  the 
circuit  to  which  it  is  attached  (see  page  40). 

Resistance. — The  resistance  should  be  appropriate  for  the 
measurement  in  hand  so  that  the  maximum  sensibility  of  method 
may  be  obtained. 

Freedom  from  Effects  of  Mechanical  Disturbances. — Great 
care  should  be  exercised  in  making  and  mounting  the  movable 
system  so  that  symmetry  about  the  axis  of  rotation  is  attained ; 
this  contributes  much  to  the  stability  of  the  system  when  it  is 
subjected  to  mechanical  disturbances.  Choice  of  location  for 
the  instrument  and  the  method  of  setting  up  are  important. 

Freedom  from  Stray-field  Effects. — It  is  essential  that  the 
indications  be  uninfluenced  by  the  unavoidable  variations  of  the 
local  field. 

Definiteness  of  Zero  Reading. — The  zero  reading  should  be 
definite  and  the  deflections  should  come  promptly  to  their  final 
values  with  no  viscous  action  of  the  controlling  spring. 

Law  of  Deflection. — Throughout  its  useful  range  the  deflection 
as  read  from  the  scale  should  be  proportional  to  the  current. 

Visibility  of  Suspended  Parts. — When  the  instrument  is  set 
up  and  ready  for  use,  it  should  be  possible  to  see  the  movable 
parts  and  to  satisfy  oneself  that  the  clearances  are  properly 
adjusted. 

Accessibility  for  Repairs. — It  should  be  possible  to  take  out 
easily  the  entire  movable  system  with  its  suspension. 

Temperature  Effects. — The  effect  of  temperature  on  the  sensi- 
tivity should  be  small  and  inequalities  of  temperature  should 
not  set  up  thermo-electric  currents  in  the  galvanometer  circuit. 

Optical  System. — The  definition  obtained  by  the  optical 
system  used  in  reading  the  deflections  should  be  so  perfect  that 
readings  to  the  limit  of  accuracy  of  the  instrument  may  be 
obtained  without  undue  fatigue. 

THE  JULIUS  DEVICE  FOR  ELIMINATING  THE  EFFECTS  OF 
MECHANICAL  DISTURBANCES  ON  GALVANOMETERS11 

The  object  to  be  attained  is  the  suspension  of  the  movable 
system  of  the  instrument  from  a  point  which  is  practically 
stationary. 


50 


ELECTRICAL  MEASUREMENTS 


The  dimensions  of  the  apparatus  which  are  given  below  have 
been  found  satisfactory. 

In  the  arrangement  there  are  two  non-magnetic  rings  13  in.  in 
diameter,  1  in.  wide  and  J£  in.  thick.  These  rings  slide  on  three 
brass  rods,  %  in.  in  diameter  and  30  in.  long,  and  can  be  clamped 
by  set  screws  at  any  desired  position.  Between  the  rings  is  a 
movable  platform  to  which  the  galvanometer  can  be  firmly 
attached. 


FIG.  19. — Julius  suspension. 

The  arrangement  is  hung  by  three  parallel  steel  wires,  about 
No.  18  B.  &  S.  gage,  from  a  three-armed  support,  attached  by 
a  single  lag  screw  to  a  bracket.  The  points  of  attachment  of  the 
three  wires  are  stout  hooks  fastened  to  the  brass  rods  so  that  the 
neck  of  the  hook  is  12%  in.  from  the  upper  end  of  the  rod.  At- 
tached to  the  hooks  are  damping  vanes  3  by  4  in.,  dipped  in  jars 
filled  with  oil ;  the  centers  of  these  vanes  are  at  the  height  of 
the  necks  of  the  hooks.  Above  the  upper  rings  are  three  iron 
weights  of  6  Ib.  each,  which  slide  on  the  rods  and  can  be  clamped 


THE  MEASUREMENT  OF  CURRENT  51 

at  any  desired  height  by  means  of  set  screws.  The  lower  ends 
of  these  rods  are  provided  with  levelling  screws.  The  weight 
of  the  arrangement  is  about  45  pounds. 

To  make  the  necessary  adjustments  the  device  is  levelled  and 
the  galvanometer  put  in  place,  levelled  and  firmly  clamped  in  posi- 
tion. The  axis  of  the  suspended  system  should  be  in  the  vertical 
axis  of  the  arrangement,  for  symmetry  is  important. 

The  platform  is  now  raised  until  the  point  of  attachment  of 
the  suspension  fiber  to  the  frame  of  the  instrument  is  in  the 
plane  passing  through  the  necks  of  the  hooks.  It  is  then  clamped 
in  position. 

The  whole  device,  galvanometer  and  all,  (it  may  be  necessary 
to  remove  the  suspended  system)  is  now  hung  by  one  of  the  hooks 
and  the  weights  adjusted  until  the  rods  which  are  normally  in  a 
vertical  position  are  truly  horizontal;  the  weights  should  be  at 
equal  distances  from  the  upper  ends  of  the  rods.  These  adjust- 
ments insure  that  the  point  of  attachment  of  the  fiber  and  the 
center  of  gravity  of  the  whole  arrangement  are  at  the  same  point 
and  in  the  plane  of  support. 

The  device  may  now  be  put  in  position,  the  three  suspension 
wires,  of  equal  length,  attached  to  the  hooks,  and  levelling 
screws  raised,  leaving  the  arrangement  freely  suspended.  It  is 
well,  for  convenience  of  adjustment,  to  attach  the  wires  to  the 
frame  at  their  lower  ends  by  small  turn-buckles.  Complete 
shielding  from  draughts  is  essential.  To  prevent  serious  results 
arising  from  the  breaking  of  the  suspension  wires  a  shelf  should 
be  placed  immediately  below  the  device. 

SHUNTS 

In  using  galvanometers,  it  is  often  found  either  that  the  instru- 
ments are  too  sensitive  or  that  their  carrying  capacities  are 
insufficient.  In  such  cases,  shunts  placed  between  the  terminals 
of  the  galvanometer  and  acting  as  bypasses  for  the  current,  are 
employed  (see  Fig.  20). 

When  zero  methods  are  used,  shunts  are  resorted  to  for  the 
purpose  of  protecting  the  galvanometers  during  preliminary  ad- 
justments. Much  time  is  thus  saved,  for  the  violence  of  the 
deflection  and  consequently  the  time  necessary  for  the  needle  to 


52 


ELECTRICAL  MEASUREMENTS 


come  to  rest  are  reduced.  A  familiar  example  of  the  use  of 
shunts  to  extend  the  range  of  galvanometers  is  found  in  direct 
current,  moving  coil  ammeters.  \ 

Where  it  is  desired  to  compute  the  total  current  in  a  circuit 
from  the  indication  of  a  shunted  galvanometer,  an  exact  knowl- 
edge of  the  resistance  of  both  shunt  and  galvanometer  at  the 
time  of  use"  is  necessary.  Attention  must  be  given  to  possible 
sources  of  error,  such  as  defective  contacts  and  changes  of  resist- 
ance due  to  temperature. 
Let  I  =  line  current. 

I0  =  galvanometer  current. 

Is  =  shunt  current. 

RG  =  resistance  of  galvanometer. 

S  =  resistance  of  shunt. 
Then 


—    is  called  the  multiplying  power  of  the  shunt.     The 


ordinary  arrangement  of  a  shunt  box  for  use 
with  a  reflecting  galvanometer  is  shown  in 
Fig.  20.  By  changing  the  position  of  the 
plug,  definite  portions,  usually  Ko>  Koo*  or 


42. 


sAA/vw^A/^^^vYv^AA^/y^A^'Wv 


FIG.  20. — Diagram  for  ordinary  shunt  box. 


FIG.  21.— Dia- 
gram for  universal 
shunt  box. 


K>ooo  of  the  total  current  can  be  sent  through  the  galvanom- 
eter, which  may  be  short-circuited  by  placing  the  plug  in  the 
last  hole  to  the  right. 

The  Ayrton-Mather  Universal  Shunt.12 — The  universal  shunt 
is  shown  diagrammatically  in  Fig.  21.  A  high  resistance, 
of  r  ohms,  is  permanently  connected  across  the  galvanometer 
terminals,  one  of  which,  TF,  is  permanently  connected  to  the 
external  circuit.  By  the  proper  arrangements,  the  other  lead 


THE  MEASUREMENT  OF  CURRENT  53 

from  the  external  circuit,  jPM,  may  be  connected  at  will  to  points  on 

r         T 

r  which  are  commonly  distant  r,  ^  VQQ»  etc.,  from  the  fixed  termi- 
nal. Referring  to  the  figure,  it  will  be  seen  that  the  line  current 
is  given  by 

(v\      1 
,                ~r 

1     —    la 


n 
For  any  particular  galvanometer  and   shunt  box  f— — — j   is 

constant.  This  factor  is  the  multiplying  power  of  the  shunt 
when  the  movable  terminal  is  at  the  extreme  right  of  r. 

It  is  seen  that  the  relative  multiplying  power  is  n.  The  values 
of  n  depend  on  the  locations  of  the  taps  by  which  the  movable 
terminal,  T M  is  connected  to  r.  They  are  independent  of  the 
relative  magnitudes  of  the  resistances  of  the  galvanometer 
and  the  shunt.  The  box  is  graduated  in  terms  of  the  relative 
multiplying  powers;  consequently  it  may  be  used  with  any 
galvanometer:  hence  the  name  universal.  However,  though  the 
multiplying  powers  are  not  affected,  the  same  shunt  box  cannot 
be  applied  indiscriminately  to  all  galvanometers  and  satisfactory 
results  attained.  For  the  maximum  current  through  the  instru- 

T 

ment  is  IG  =  I  -^ —  —     Therefore,  in  order  that  practically  the 
KG  ~r  r 

full  sensitivity  of  the  galvanometer  may  be  realized,  r  must  be 
much  larger  than  RG;  if  it  is  nine  times  the  galvanometer  resist- 
ance, 90  per  cent,  of  the  sensitivity  may  be  realized.  Again,  if 
r  is  too  small,  and  a  moving  coil  galvanometer  is  employed,  the 
instrument  will  be  over-damped  and,  therefore,  sluggish  in  its 
action. 

The  distinct  advantage  of  the  universal  shunt  box  is  that  when 
it  is  used  in  open-circuit  work,  any  damping  due  to  currents  set 
up  by  the  motion  of  either  the  needle  or  the  movable  coil  of  the 
galvanometer  is  constant.  This  is  especially  important  when 
capacities  are  being  compared  by  means  of  the  ballistic  galva- 
nometer. 

Also,  when  a  universal  shunt  is  used  with  a  moving-coil  galva- 
nometer in  a  circuit  of  very  high  resistance,  it  is  possible,  by  prop- 
erly choosing  r,  to  render  the  galvanometer  dead  beat  for  all 


54  ELECTRICAL  MEASUREMENTS 

values  of  the  multiplying  power.     Such  a  case  arises  when  insula- 
tion resistances  are  being  measured. 

AMMETERS 

. 

An  ammeter,  in  distinction  from  a  galvanometer,  is  an  instru- 
ment so  constructed  that  the  current  strength  in  amperes  can  be 
read  directly. 

Before  referring  to  various  designs  of  these  instruments,  it 
will  be  well  to  refer  to  certain  considerations  which  have  influ- 
enced the  development  of  indicating  electrical  instruments, 
especially  for  direct-current  work. 

1.  The  resistance  of  all  current-measuring  instruments  should 
be  very  low,  while  that  of  all  instruments  for  measuring  voltages 
should  be  as  high  as  practicable,  the  reason  in  both  cases  being 
that  the  disturbance  of  the  circuit  conditions  by  the  insertion  of 
the  instrument  must  be  reduced  to  a  minimum.     Another  way  of 
stating  the  same  thing  is  that  the  energy  dissipated  in  the  instru- 
ment must  be  a  minimum. 

2.  The  construction  must  be  such  that  the  instrument  will 
maintain  its  reliability.     The  relative  positions  of  the  parts  must 
be  maintained  in  spite  of  rough  handling  and  the  strength  of  all 
magnets  used  must  be  insured  by  proper  ageing. 

3.  There  must  be  no  "set"  of  the  controlling  springs  due  to 
standing  under  load  and  no  indefiniteness  of  the  zero  reading  due 
to  magnetic  impurities  in  the  movable  coils. 

4.  The  indications  of  the  instrument  must  be  independent  of 
stray  fields.     The  importance  of  this  in  industrial  testing  cannot 
be  over-emphasized. 

5.  The  indications  must  be  independent  of  room  temperature 
and  no  errors  must  result  from  the  heating  due  to  the  passage 
of  the  current. 

6.  All  shunts  must  be  free  from  errors  due  to  thermo-electro- 
motive  forces. 

7.  Ammeter  shunts  must  be  so  constructed  that  they  will  not 
be  injured  by  abnormal  currents  of  short  duration  and  ample 
provision  must  be  made  for  dissipating  the  heat  due  to  continuous 
operation. 

8.  There  must  be  no  effects  due  to  the  retentiveness  of  any 


THE  MEASUREMENT  OF  CURRENT  55 

soft  iron  parts,  for  this  causes  the  indications  of  the  direct- 
current  instruments  to  depend  on  their  previous  history. 

9.  Pivot  friction  must  be  reduced  to  a  minimum  and  the  mov- 
ing system  properly  balanced. 

10.  The  instrument   must   be   dead   beat,  that  is,  critically 
damped,  in  order  that  fluctuations  of  the  load  may  be  followed 
with  certainty  and  that  the  time  necessary  for  taking  readings 
may  be  reduced  to  a  minimum. 

11.  The  graduation  should  be  convenient.     This  reduces  the 
liability  to  mistakes  in  readings  which  have  to  be  taken  hurriedly. 

Moving-coil  Ammeters. — In  direct-current  instruments,  the 
fulfilment  of  the  conditions  stated  above  is  most  readily  obtained 
by  employing  the  moving-coil  principle. 

The  first  thoroughly  practical  instrument  of  this  class  was 
designed  by  Edward  Weston  in  1888.  It  will  be  described,  in 
its  present  form,  as  a  typical  example  of  a  moving-coil  ammeter. 

Weston  Standard  Portable  Ammeter. — This  instrument  is 
essentially  a  shunted  D'Arsonval  galvanometer,  so  designed  that 
it  fulfils  the  requirements  of  portability  and  general  reliability. 

The  magnet,  which  is  of  the  horseshoe  type,  is  made  of  tungsten 
steel  and  is  artificially  aged;  the  cross-section  is  about  1.25  by 
0.3  in.  Carefully  shaped  soft-iron  pole  pieces  are  attached  to 
the  magnet  by  screws  so  that  the  space  between  them  is  cylin- 
drical. In  this  space  is  placed  a  soft  iron  cylinder  supported 
from  a  brass  yoke  attached  to  the  pole  pieces.  The  air  gap  is 
about  0.04  in.  wide;  consequently,  the  coil  moves  in  a  radial 
field  (see  page  35).  The  movable  coil,  of  copper,  is  wound  on 
an  aluminum  frame  which  also  serves  as  a  damping  device  to 
make  the  instrument  dead  beat.  •  The  movable  system  is  pro- 
vided with  steel  pivots  which  turn  in  two  jewelled  (sapphire) 
bearings  which  are  carried  by  non-magnetic  yokes  attached  to 
the  pole  pieces  in  such  a  manner  that  the  coil  is  truly  centered. 
The  directive  force  is  given  by  two  flat  spiral  springs,  one  above 
and  one  below  the  coil;  they  are  made  of  non-magnetic  material 
and  also  serve  as  leads  to  the  movable  coil.  The  inner  ends  of 
the  springs  are  attached  to  brass  collars  which  form  the  terminals 
of  the  coil,  the  outer  ends  to  the  extremities  of  two  insulated 
crossarms  which  can  be  moved  coaxially  with  the  coil,  to  adjust 
the  zero.  In  the  more  recent  instruments  this  adjustment  may 


56 


ELECTRICAL  MEASUREMENTS 


be  made  without  opening  the  case,  by  turning  a  slotted  head 
at  the  front  of  the  base.  The  pointer  is  an  aluminum  tube 
flattened  at  the  index  end.  The  moving  parts  are  balanced  by 
three  adjustable  counterweights  on  short  arms  which  project  at 
right  angles  to  the  axis  of  rotation  and  are  in  the  plane  of  motion 
of  the  pointer;  adjustment  is  made  by  moving  the  weights  along 
the  arms.  Parallax  is  eliminated  by  the  use  of  a  mirror  beneath 
the  pointer. 


To  Lower  Spring       To  Upper  Spring 


Line 


Line 


FIG.  22. — Diagram  for  Western  moving-coil  ammeter. 

The  graduation  of  the  scale  is  practically  uniform,  but  no  par- 
ticular law  of  deflection  is  assumed.  The  principal  points  are 
determined  by  comparison  with  a  standard  instrument  and  the 
subdivision  is  done  by  a  dividing  engine. 

A  small  resistance  coil  is  included  in  the  galvanometer  circuit, 
and  the  final  adjustment  is  made  by  altering  its  resistance. 

For  self-contained  portable  instruments,  the  present  practice 
of  the  Weston  Instrument  Co.  is  to  use  in  milliammeters,  up  to 


THE  MEASUREMENT  OF  CURRENT 


57 


1,500  milliamp.,  a  drop  of  approximately  150  millivolts  at  full- 
scale  deflection.  In  ammeters  having  ranges  from  2  to  150  amp., 
the  drop  is  about  50  millivolts;  for  ranges  from  200  to  500  amp., 
it  is  35  millivolts.  In  all  external  shunts  of  the  new  type  the 
drop  is  approximately  100  millivolts  and  in  the  switchboard 
shunts  it  is  about  50  millivolts. 

In  self-contained  instruments  the  shunts  are  mounted  in  the 
base  which,  if  the  current  capacity  is  considerable,  is  properly 
ventilated.  For  large  currents  the  best  procedure  is  to  separate 
the  millivoltmeter  and  the  shunt  and  mount  them  in  different 
cases;  this  allows  the  shunt  to  be  designed  so  that  the  heat  is 
readily  dissipated.  An  external-shunt  instrument  gives  a  flexible 
arrangement  very  convenient  for  general  testing,  for  shunts  of 
different  ranges  may  be  used  with  the  same  millivoltmeter. 


FIG.  23. — Switchboard  shunt. 

In  using  any  form  of  shunt  and  millivoltmeter,  it  is  necessary 
to  calibrate  and  to  use  the  instrument  with  the  same  set  of  leads 
connecting  the  shunt  and  the  millivoltmeter  and  to  avoid  all 
extraneous  resistances  in  the  leads  due  to  imperfect  contacts  at 
the  terminals. 

The  moving-coil  principle  is  now  universally  employed  in  the 
best  makes  of  direct-current  instruments.  Separate  millivolt- 
meters  and  shunts  are  universally  used  in  direct-current  switch- 
board work.  The  shunts  are  put  at  any  convenient  point  in  the 
busbars  and  small  leads  are  run  to  the  indicating  part  which  is 
on  the  front  of  the  switchboard.  This  greatly  simplifies  the  con- 
struction of  the  board  and  reduces  expense. 

Fig.  23  shows  a  switchboard  shunt.  It  will  be  noted  that  the 
resistance  strips  are  very  short  and  are  soldered  into  massive 


58  ELECTRICAL  MEASUREMENTS 

terminal  blocks  which  can  be  interleaved  with  the  busbar.  The 
heat  is  thus  disposed  of  by  conduction  as  well  as  by  convection. 

Reference  should  be  had  to  the  introduction  to  the  chapter  on 
the  " Calibration  of  Instruments"  where  various  errors  found  in 
commercial  ammeters,  voltmeters,  etc.,  are  discussed. 

Thermo -ammeters. — The  rise  of  temperature  of  a  wire  carrying 
a  current  is  a  function  of  the  current  strength ;  it  may  be  utilized 
for  purposes  of  measurement.  Various  forms  of  indicators  have 
been  devised.  They  utilize  the  change  of  electrical  resistance  of 
the  wire,  its  expansion,  or  its  rise  of  temperature. 

For  alternating-current  work  the  hot-wire  or  thermal  principle 
possesses  certain  theoretical  advantages,  due  to  the  fact  that 
there  are  neither  coils  nor  soft  iron  in  the  instruments;  hence, 
inductance  effects  are  reduced  to  a  minimum  and  saturation 
effects  eliminated  altogether.  With  proper  design  such  instru- 
ments should  then  be  applicable  to  both  direct-  and  alternating- 
current  circuits  and  their  indications  should  be  independent  of 
frequency,  wave  form,  and  stray-field  effects. 

The  practical  difficulties  met  with  are  due  to  the  uncertainty 
of  the  zero  reading,  to  the  sluggishness  of  action  due  to  the  heat 
capacity  of  the  various  parts  of  the  instrument  and  to  the  influ- 
ence of  room  temperature.  Also,  as  the  carrying  capacity  of 
the  hot  wire  is  seriously  taxed,  there  is  the  liability  of  burning 
out  the  instrument  by  a  temporary  overload  or  short-circuit, 
which  in  the  ordinary  type  of  instrument  would  result  in  nothing 
worse  than  a  bent  pointer.  Usually  the  energy  consumption  in 
this  class  of  instruments  is  large. 

All  things  considered,  hot-wire  instruments  are  unsuited  for 
switchboard  work.  Their  particular  field  of  usefulness  is  in  high- 
frequency  work,  such  as  radio-telegraphy  or  in  the  laboratory 
where  they  are  employed  as  " crossover"  instruments  between 
alternating  and  direct  currents  in  calibration  work. 

At  ordinary  frequencies  shunts  may  be  employed,  but  for 
switchboard  work  no  great  advantage  results  from  this,  for  in 
American  practice  all  alternating-current  instruments  on  circuits 
of  above  500  volts  are  actuated  through  transformers,  thus  keep- 
ing the  front  of  the  switchboard  free  from  high-voltage  circuits 
which  would  be  a  source  of  danger. 

The  earliest  commercial  instrument  based  on  the  thermal  01 


THE  MEASUREMENT  OF  CURRENT  59 

hot-wire  principle  was  the  voltmeter  invented  by  Major  Cardew, 
R.  E.  In  this  instrument  the  expansion  of  a  long  platinum  wire 
due  to  the  passage  of  the  current  caused  the  pointer  to  move  over 
the  scale.  The  more  recent  form  of  hot-wire  instrument  made 
by  Hartmann  and  Braun  is  shown  in  Fig.  24.  Its  distinguishing 
feature  is  the  exceedingly  ingenious  method  of  multiplication  by 
which  the  small  expansion  of  a  short  wire  is  caused  to  produce  a 
large  deflection  of  the  pointer,  without  the  use  of  levers,  knife 
edges,  or  gears. 

A  and  B  are  lugs  carried  by  a  composite  metal  frame,  the  length 
of  the  iron  and  brass  parts  being  such  that  the  frame  is  designed 


FIG.  24. — Diagram  for  Hartmann  and  Braun  hot-wire  ammeter. 

to  have  the  same  coefficient  of  expansion  as  the  wire  AB.  The 
lug  G  is  carried  by  a  portion  of  the  frame  having  the  same  coeffi- 
cient of  expansion  as  the  wire  DC.  An  inextensible  cord,  EG, 
passes  once  around  the  drum,  F,  to  which  the  pointer  is  attached, 
and  is  drawn  taut  by  the  spring  S. 

The  current  flows  through  the  wire  AB,  which  is  heated  and 
expands;  the  slack  is  taken  up  by  the  spring  and  the  pointer  is 
moved  over  the  scale.  The  zero  reading  may  be  adjusted  by 
the  screw  a. 

The  wire  AB  is  of  platinum-iridium.  This  has  a  smaller  coeffi- 
cient of  expansion  but  a  higher  melting  point  than  the  platinum- 
silver  wire  formerly  used.  It  may  thus  be  worked  at  a  higher 
temperature  and  gives  less  trouble  from  variations  of  room 
temperature. 

For  work  at  ordinary  frequencies  the  range  of  the  indicator 
is  extended  by  the  use  of  shunts.  This  is  of  importance  in  labora- 


ELECTRICAL  MEASUREMENTS 


tory  work,  for  the  shunted  instrument  may  be  calibrated  with 
direct  and  used  with  alternating  currents.  ' 

To  increase  the  current  capacity  of  this  form  of  indicator  the 
wire  AB  may  be  sectionalized,  as  indicated  in  Fig.  25. 

The  connections  to  AB  at  1,  2,  3,  are  made  with  thin  strips  of 

silver  foil  so  that  the  motion  is 

x"» 

pi  not  impeded. 

The  current  capacity  of  the 
B  indicator  is  about  5  amp.,  the 
resistance     about    0.05    ohm, 
consequently  the  full-load  drop 
is    approximately    250     milli- 
volts, or  about  three   or  four 
times    that    in    the    ordinary 
direct-current   switchboard   shunt. 

As  the  resistance  is  so  low,  it  is  essential  that  all  connections 
between  the  indicator  and  the  shunt  be  carefully  made  and  that 
the  same  set  of  leads  connecting  the  indicator  and  the  shunt 
be  used  during  calibration  and  subsequent  use  of  the  ammeter. 

The  Duddell  Thermo -ammeter. — The  working  parts  of  this 
modification  of  the  thermo-galvanometer  (see  page  46)  are 

Zero  Set 


FIG.    25. — Sectionalized  wire  for  hot- 
wire ammeter. 


Lower  Pivot  and  Guide  Jewel 

ermo  Junction 
Receiving  Plate 
Heater 

FIG.  26. — Diagram  for  Duddell  thermo -ammeter. 

shown  in  Fig.  26. ,  The  movable  coil  is  so  mounted  that  it  is 
practically  supported  from  the  upper  pivot,  the  lower  pivot  act- 
ing largely  as  a  guide.  Pivot  friction  is  thus  minimized. 

The  instrument  is  primarily  designed  for  measurements  at 


THE  MEASUREMENT  OF  CURRENT      61 

high  periodicity,  such  as  occur  in  telephonic  work  or  in  wireless 
telegraphy. 

The  standard  resistances  of  the  heaters  are  2  and  150  ohms, 
the  latter  for  telephonic  work.  A  full-scale  deflection  can  be 
obtained  with  a  current  of  about  10  milliamp.  Consequently 
the  power  taken  by  the  instrument  is  about  0.015  watts  at  full- 
scale  reading. 

To  obtain  a  compact  heater  for  use  with  currents  below  20 
milliamp.  a  deposit  of  platinum  on  mica  is  used,  the  platinum 
being  scraped  away  to  form  a  grid.  A  resistance  of  several 
hundred  ohms  may  thus  be  obtained  in  a  space  of  less  than  0.2 
sq.  cm.  For  larger  currents  a  wire  heater  is  used.  In  either 
case  the  self-induction  and 
capacity  are  so  small  as  to  be 
negligible  in  their  effects. 

High-frequency  Ammeters.13 
— By     proper      design     the 
thermo-ammeter       may     be 

adapted  to  the  measurement    FIG.  27.— High-frequency  ammeter  for 

f    i  i  •   i    f  small  currents, 

of  large  high-frequency   cur- 
rents, such  as  occur  in  radio-telegraphy. 

An  instrument  for  small  high-frequency  currents  is  shown  in 
Fig.  27.  The  entire  current  flows  through  the  wire  AB,  which 
for  currents  up  to  0.3  amp.  may  be  a  Eureka  wire  0.05  mm.  in 
diameter.  The  skin  effect  in  this  wire  at  1,000,000  cycles  is 
less  than  0.001  per  cent.  For  currents  up  to  1.2  amp.  a  copper 
wire  0.08  mm.  in  diameter  is  used.  In  this  the  skin  effect  at 
1,000,000  cycles  is  less  than  0.3  per  cent.  The  temperature  of  the 
wire  is  determined  by  a  thermo-electric  junction.  The  indicator 
may  be  a  moving  coil  galvanometer  connected  between  the 
binding  posts. 

Instruments  for  small  currents  present  no  difficulties.  The 
trouble  arises  when  it  is  necessary  to  have  a  large  carrying  capac- 
ity. In  this  case,  two  or  more  wires  must  be  used  in  parallel 
and  the  difficulty  comes  from  the  fact  that  the  current  may  not 
divide  properly  between  the  wires. 

The  heating  in  all  the  wires  should  contribute  to  the  functioning 
of  the  indicator.  Then  the  errors  due  to  the  improper  distribu- 
tion of  the  current  are  much  decreased,  for  though  the  total  heat 


62 


ELECTRICAL  MEASUREMENTS 


production  changes  with  the  distribution  of  the  current,  the 
change  is  less  than  the  change  in  the  current  distribution  itself. 
The  reading  of  any  ammeter  which  depends  on  the  whole  heat 
production  will  either  remain  constant  or  increase  as  the  fre- 
quency is  increased. 

A  two-wire  instrument  where  the  total  heat  production  is 
utilized  is  shown  diagrammatically  in  Fig.  28. 

The  high-frequency  current  is  taken  in  through  the  leads  Aa 
and  Bb  which  are  perpendicular  to  the  active  wires  ACB  and 
ADB,  which  are  of  copper  and  0.1  mm.  in  diameter. 


FIG.  28. — Two-wire  ammeter  for  high-frequency  currents. 

The  points  C  and  D  are  located  so  that  the  arrangement  is  as 
nearly  as  possible  a  Wheatstone  bridge.  The  high-frequency 
current  is  thus  kept  out  of  the  auxiliary  bridge  which  is  used  for 
measuring  the  resistance.  As  the  location  of  C  and  D  may  not 
be  exact,  it  is  preferable  to  use  a  low-frequency  alternating  cur- 
rent instead  of  direct  current  in  calibrating  the  arrangement. 
In  order  to  eliminate  the  effects  of  thermal  e.m.fs.  the  gal- 
vanometer is  used  on  closed  circuit.  This  arrangement  when 
immersed  in  oil  has  a  capacity  of  10  amp. 


THE  MEASUREMENT  OF  CURRENT  63 

The  Parallel-wire  Ammeter. — In  this  form  of  instrument  the 
conductor  is  a  group  of  several  straight  wires  of  the  same  length 
and  diameter  and  so  fine  that  changes  of  resistance  due  to  skin 
effect  are  negligible;  they  are  parallel  in  direction  and  usually 
are  equally  spaced. 

A  typical  arrangement  of  this  sort  is  shown  in  Fig.  29.  The 
current  is  led  in  through  the  heavy  terminals  which  are  perpen- 
dicular to  the  active  wires  and  therefore  exercise  no  inductive 
effect  on  them.  The  distributing  terminals  at  the  ends  of  the 
parallel  wires  have  a  negligible  impedance. 

In  a  perfect  instrument  all  the  wires  will  have  the  same 
resistance  and  a  direct  or  low-frequency  current  will  divide 
equally  between  them,  all 
inductance  effects  being  neg- 
ligible. At  very  high  fre- 
quencies the  distribution  of 
current  between  the  wires  is 
determined  by  the  induc- 
tances, self  and  mutual, 
rather  than  by  the  resis- 
tances. SO  that  it  may  be  FlG-  29.— Parallel-wire  high-frequency 

,._          .    ,.  ,.  ammeter, 

very  different  from  the  di- 
rect-current distribution;  that  is,  the  current  distribution  may 
be  a  function  of  the  frequency. 

It  is  essential  that  the  wires  be  of  uniform  resistance.  Lack  of 
uniformity  may  be  due  to  variation  in  hardness  or  small  varia- 
tions in  the  cross-section.  These  things  will  not  affect  the  induc- 
tances, so  the  wires  may  carry  equal  currents  at  high  frequencies 
but  very  different  currents  at  low  frequencies  where  the  resistance 
effects  preponderate. 

If  the  indicator  is  attached  to  one  wire,  as  in  Fig.  29,  the 
magnitude  of  the  error  will  depend  on  which  wire  is  used.  It 
will  be  decreased  if  the  arrangement  is  such  that  all  the  wires 
contribute  to  the  functioning  of  the  indicator,  for  if  the  current 
in  one  wire  is  decreased,  that  in  the  others  must  correspondingly 
increase  and  the  change  in  the  total  heat  production  is  much  less 
than  that  in  any  one  wire.  Dellinger  cites  the  case  of  a  seven- 
wire  instrument,  the  indicator  of  which  was  operated  by  one  of 
the  wires  somewhat  distant  from  the  others.  At  100,000  cycles 


64  '  ELECTRICAL  MEASUREMENTS 

it  gave  readings  10  per  cent,  high,  and  at  750,000  cycles,  46  per 
cent,  high  (see  page  67). 

The  explanation  of  the  distribution  errors  will  be  seen  by 
examining  the  theory  of  the  three-wire  instrument  shown  in 
Fig.  29,  where  the  arrangement  is  such  that  these  errors  are 
pronounced. 

SYMBOLS  USED  AND  THE  DATA  FOR  A  PARTICULAR  CASE 

I  =  length  of  wires,  10.00  cm. 
5  =  diameter  of  wires,  0.008  cm. 
d  =  distance  between  wires,  0.40  cm. 
Ra  =  mean  resistance  of  a  and  a',  0.347  ohm 
Rb  =  resistance  of  b,  0.352  ohm. 

L  =  coefficient  of  self-induction  of  one  wire,  155.00  cm. 
Mob,  Ma'6,  Mao'  =  coefficients  of  mutual  induction. 
Mab  =  Ma'b  by  symmetry. 

v  =  instantaneous  potential  difference  between  the  ends  of 

the  wires. 

i  =  total  instantaneous  current. 
ia,  iaf,  ib  =  instantaneous  currents  in  Ihe  wires. 

It  will  be  necessary  to  calculate  the  self-inductance  of  the 
straight  wires  by  the  approximate  formula 


L  =  21  jloge^  -  0.75). 
The  mutual  inductance  will  be  given  by 


L  =  20  I  log,  -n~n°nQ  -  0.75}  =  155  cm. 

I  U.UUo  J 

=  20  j  log,  -oJ-1  +i()!  =  59.0 

on  Q  o  i 

log,         -  1  +     ^     =  46.0 


The  potential  difference  between  the  ends  of  the  wires  will  be 

diaf 


.  a 

V    =    Ra^a   +  L~ 


di 


b    .    ,,       a    .    ,,-        a' 
=  Rb^b  +  It-     +  Mab       +  M*ir     • 


THE  MEASUREMENT  OF  CURRENT  65 

If  Ra  =  Ra',  then  by  symmetry  ia  =  ia>  and  i*  =  i  —  2ia. 
Making  this  substitution  and  arranging  terms 

(Ra  +  2Rb)ia  +  (3L  +  Maa>  -  4Mab)~~  =  Rbi  +  (L  -  Mafe)^ 
Assuming  sinusoidal  currents 
(Ra  +  2Rb)Ia  +>(3L  +  Maa,  -  4Mab)Ia 

=  Rbl'+ju(L  -  Mab)I        (36) 


{Rf  +  co2(L  - 
Solving  for  I\ 


\P         (37) 

At  low  frequencies,   denoted  by  the  subscript  0,  where  the 
inductance  effects  are  negligible, 

?7V  =  2  +  W  -  2'986  (36°^ 

(lajQ  Kb 

and 

(        =  1  +  2       =  3.029  (37o) 


At  frequencies  so  high  that  the  resistance  effects  are  swamped 
by  those  of  inductance,  these  ratios  become 
/  __  3L  +  Maa,  -  4Ma, 

Ta    ~  ~1T-  ~M^~ 


_ 

aa  -        ^  " 
and 

Ia  L  —  Mab 

T  =T  -----  ^F~    ~~'*W~  =  1-156  (40) 

Ib     L  +  AZ  ao/  —  2Afa& 

From  the  data  given,  at  any  frequency,  /,  by  (36)  and  (37) 


0  124  4- 

^^  ~^— —  "  ~~ ^ .  /^ i  \ 

.105  +  2.98    X  10~12/2 


0^2^+0.272  X  10- 12/2 
.105  +  2.98    X  10- 12/2  ^     ^ 


66 


ELECTRICAL  MEASUREMENTS 


Combining  (41)  and  (36o)  and  (42)  and  (37a)  and  assuming 
that  the  same  total  current  flows,  70  =  /, 


-  =  2.986 


Wo 


=  3.029  U  -£ 


(43) 


(44) 


The  results  obtained  by  using  these  formulae  are  compared 
with  the  experimental  results  in  the  following  table.  The  agree- 
ment is  as  good  as  the  experimental  accuracy  warrants. 

TABLE  SHOWING  DISTRIBUTION  IN  A  THREE- WIRE  HIGH-FREQUENCY 
AMMETER.    ALL  THREE  WIRES  IN  SAME  PLANE 


Frequency 

Per  cent,  increase  of  current 
in  (a) 

Per  cent,  decrease  of  current 
in  (6) 

Calculated 

Observed 

Calculated 

Observed 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

150,000 

0.3 

0.4 

0.6 

0.2 

500,000 

1.8 

1.3 

3.4 

3.0 

1,000,000 

3.1 

2.8 

6.1 

5.3 

1,500,000 

3.9 

3.6 

7.4 

6.0 

CO 

4.3 

8.5 

From  the  table  it  is  seen  that  the  changes  in  distribution  are 
practically  confined  to  the  frequencies  between  100,000  and 
1,500,000.  That  is,  the  range  of  frequencies  in  which  the  changes 
of  distribution  occur  is  that  used  in  radio-telegraphy.  Extreme 
effects  of  change  in  current  distribution  are  shown  in  Fig.  30, 
which  applies  to  the  seven-wire  arrangement  there  shown. 

The  Use  of  High  Resistance  Wires. — The  distribution  errors 
may  be  minimized  by  using  wires  of  high  resistivity,  keeping 
their  lengths  and  diameters,  and  therefore  their  inductances,  the 
same.  For  example,  suppose  all  the  resistances  in  equation 
(43)  were  increased  to  30  times  their  original  values,  then 


11L6  +  0.363  X  10~12X/.2 
994.5 


(2.986). 


2.98  X  10~12  X 
Practically,  the  value  of  the  radical  is  now  determined  by  the 


THE  MEASUREMENT  OF  CURRENT 


67 


resistance  terms,  the  variable  or  reactance  term  being  almost 
negligible  for  the  range  of  frequencies  used  in  radio-telegraphy. 
At  1,000,000  cycles 

A-  =  1.0005 

UaJQ 

instead  of  the  value  77^-  =  1.032  which  obtains  when  low  re- 

U«Jo 

sistance  wires  are  used. 


ICopp 
_Stri 


pper 
P 


>5]G-M- 


DIAGRAM  FOR  A  SEVEN  WIRE  INSTRUMENT 


02468 

Amperes 

FIG.  30. — Plot  showing  distribution  errors  in  a  seven-wire  high-frequency 
ammeter.     All  seven  wires  in  the  same  plane. 

The  Utilization  of  the  Whole  Heat  Production.— It  has  been 
stated  that  it  is  important  that  the  whole  heat  production  con- 
tribute to  the  operation  of  the  indicator.  This  may  be  illustrated 
by  reference  to  the  three-wire  instrument.  Assume  that  with 
direct  currents,  10  amp.  flows  in  each  of  the  wires;  assuming  them 
to  be  of  equal  resistance,  the  total  heat  production  will  be  pro- 
portional to  102  +  102  -1-  102  =  300.  At  1,000,000  cycles  the 
currents  will  be  approximately  10.3,  9.4,  10.3,  and  the  total  heat 


68 


ELECTRICAL  MEASUREMENTS 


production  will  be  proportional  to  (10.3) 2  +  (9.4) 2  -f  (10.3) 2  = 
300.6,  a  change  of  0.2  per  cent.  But  the  change  in  heat  produc- 
tion in  wire  a  is  from  100  to  106.1  or  over  6  per  cent,  and  that  in 
wire  6  is  from  100  to  88.4,  a  change  of  over  11  per  cent.  To 
take  advantage  of  this  total  heat  production  the  thermo-electric 
arrangement  may  be  altered. 

A  fine  Eureka  wire  may  be  soldered  between  a  and  b  and  a 
copper  wire  between  6  and  a'.  The  lead  from 
Ti  to  a  is  of  copper,  that  from  Tz  to  a'  of 
Eureka  wire. 

Sectionalized  Wires. — High-frequency  am- 
meters in  which  the  carrying  capacity  is  in- 
creased by  sectionalizing  the  wire,  as  shown 
in  Fig.  25,  may,  contrary  to  general  belief, 
show  distribution  changes  due  to  the  self  and 
mutual  inductions  of  the  various  parts.  The 
location  of  the  leads  A  and  B  plays  an  im- 
portant part  in  these  changes;  they  should  be  symmetrically 
placed.  However,  as  all  the  sections  of  the  wire  contribute  to 
the  deflection,  that  is,  as  the  indication  depends  on  the  total 
heat  production,  the  resultant  error  is  small  though  appreciable. 
Wires  of  high  resistance  will  eliminate  the  trouble. 

Use  of  Strips. — A  favorite  method  of  obtaining  large  current 
capacity  is  to  employ  a  thin  strip,  of  high  resistivity,  soldered 


/T 

7\ 


FIG.  31.— Thermo- 
functiqn  arrange- 
ment for  utilizing 
whole  heat  produc- 
tion in  a  high-fre- 
quency ammeter. 


FIG.  32. — Roller's  arrangement  of  terminals  for  high-frequency  ammeter. 

between  massive  terminal  blocks.     With  a  high-resistance  strip 

the  errors  in  this  class  of  instruments  are  due  to  the  effects  of  the 

f 

terminal  blocks  on  the  current  distribution,  the  inductances  of 
the  current  paths  being  the  determining  factors.  These  effects 
are  avoided  by  the  arrangement  suggested  by  F.  W.  Roller, 
shown  in  Fig.  32.  Each  part  of  the  strip  has  about  the  same 


THE  MEASUREMENT  OF  CURRENT 


69 


amount  of  the  terminal  rod  in  series  with  it.  Up  to  a  frequency 
of  750,000  cycles  no  distribution  error  could  be  detected. 

A  theoretically  perfect  arrangement  of  the  terminal  blocks  is 
that  shown  in  Fig.  33.  Everything  is  symmetrical  about  a 
central  axis  along  which  the  current  enters  and  leaves. 

The  conductors  are  thin  strips  or  wires  soldered  between  the 
terminal  blocks;  this  makes  the  mutual  inductance  of  each  wire 
with  respect  to  the  others  the  same.  Of  course  the  self-induc- 
tances of  all  the  wires  will  be  equal. 

This  symmetry  insures  that  high-frequency  currents  will 
divide  equally  among  the  wires.  The  practical  difficulty  is  to 


/r> 


((  ) 

S  1 

FIG.  33. — Arrangement  of  parallel-wire  conductor  for  avoiding  distribution 
errors  in  high-frequency  ammeters. 

get  all  the  fine  wires  of  the  same  resistance.  If  this  is  not 
done,  there  will  be  changes  of  distribution  in  passing  from  low  to 
high  frequencies.  This  construction  is  used  by  Hartmann  and 
Braun. 

SOFT-IRON  INSTRUMENTS 

The  first  ammeters  and  voltmeters  used  for  commercial  meas- 
urements on  electric  light  and  power  circuits  were  of  the  soft- 
iron  type,  instruments  in  which  an  iron  core  is  drawn  into  a 
solenoid,  in  opposition  to  the  action  of  either  gravity  or  a  con- 
trolling spring. 

As  the  induced  pole  reverses  in  sign  with  reversal  of  the  cur- 
rent, a  soft-iron  instrument  deflects  in  but  one  direction,  irre- 
spective of  the  direction  of  the  current  through  it. 

The  law  connecting  the  current  and  the  pull  of  a  solenoid  on 
an  iron  core  depends  on  the  degree  of  saturation  of  the  iron. 


70  ELECTRICAL  MEASUREMENTS 

Suppose  the  core  to  remain  fixed  in  position.  If  it  is  but  weakly 
magnetized  by  the  current,  the  strength  of  the  induced  pole  will 
be  roughly  proportional  to  the  current.  This  pole  reacts  with 
the  field  of  the  solenoid  which  is  proportional  to  the  current;  so 
the  attraction  is  approximately  proportional  to  the  square  of  the 
current.  If  the  magnetizing  field  is  so  strong  that  the  core  is 
" saturated,"  any  further  increase  of  the  current  alters  the 
strength  of  the  induced  pole  but  little  and  the  attraction  is 
approximately  proportional  to  the  current. 

Thus,  as  the  current  is  gradually  increased  from  zero  to  a  high 
value,  the  law  of  the  pull  changes  from  that  of  the  square  to 
that  of  the  first  power  of  the  current,  and  the  pull  is  also  modified 
by  the  change  in  the  position  of  the  iron  core  due  to  the  yielding 


FIG.  34. — Illustrating  principle  of  magnetic-vane  instruments. 

of  the  spring  or  gravity  control.  The  net  result  is  that  the  scales 
of  direct  current  soft-iron  instruments  are  not  uniformly  divided. 

The  quality  of  the  iron  is  important.  In  order  that  the  indi- 
cations be  independent  of  the  previous  magnetic  history  of  the 
iron,  it  should  be  as  free  from  hysteresis  as  possible.  For  direct- 
current  work  soft-iron  instruments  are  now  employed  where 
cheapness  and  robustness  of  construction  are  essential  and  a 
moderate  accuracy  will  suffice. 

In  alternating-current  work  this  construction  is  employed  in 
ammeters  where  its  use  avoids  the  necessity  of  taking  large 
currents  into  the  movable  parts  of  the  instrument.  • 

Magnetic -vane  Instruments. — The  principle  involved  in  the 
magnetic-vane  instruments  is  sufficiently  illustrated  by  Fig.  34. 

As  shown  in  the  figure,  E  is  a  soft-iron  vane  fixed  to  the  spindle 


THE  MEASUREMENT  OF  CURRENT  J 


71 


which  carries  the  pointer  and  the  inner  end  of  the  controlling 
spring. 

On  the  passage  of  the  current  through  the  coil  CD,  in  which 
the  above  arrangement  is  inserted,  the  iron  is  magnetized,  the 
like  poles  repel  each  other  and  the  needle  is  moved  over  the  scale. 
An  air  damper  is  usually  added. 

There  are  many  variations  on  this  fundamental  design,  which 
is  used  for  both  ammeters  and  voltmeters. 

Weston  Soft-iron  Instruments. — In  the  Weston  soft-iron 
instruments  the  arrangement  is  as  indicated  by  Fig.  35. 

A  thin  piece  of  soft  iron 
abc  of  the  form  shown  is 
bent  to  conform  to  a  cylin- 
der; de  is  another  thin  piece 
of  iron  of  rectangular  form 
so  bent  that  it  is  coaxial  with 
abc.  It  is  rigidly  attached  to 


FIG.  35. — Weston  soft-iron  instrument. 

the  spindle.  The  coil  has  a  large  opening  at  the  center  in  which 
this  arrangement  is  placed  with  the  spindle  coinciding  with  the 
axis. 

On  the  passage  of  the  current  the  neighboring  edges  of  the 
iron  are  similarly  magnetized,  the  like  poles  repel  each  other  and 
the  index  is  forced  over  the  scale.  This  construction  is  employed 
in  both  ammeters  and  voltmeters  intended  for  use  with  alternat- 
ing currents. 

The  General  Electric  Co.'s  Inclined-coil  Ammeter.^-Referring 
to  Fig.  36,  the  current  flows  through  the  coil  which  is  inclined 
at  an  angle  of  about  45°  to  the  spindle  which  carries  the  iron 


72 


ELECTRICAL  MEASUREMENTS 


vanes  a,  6,  and  the  pointer.  When  no  current  is  passing,  the 
plane  of  the  vanes  makes  a  slight  angle  with  that  of  the  coil;  on 
the  passage  of  the  current  the  vanes  tend  to  place  themselves 
along  the  lines  of  force,  that  is,  perpendicular  to  the  plane  of  the 

coil. 

By  adopting  the  inclined  coil 
arrangement,  a  long  scale  is  ob- 
tained, for  in  order  to  turn  the 
plane  of  the  soft  iron  from  a 
position  coincident  with  the 
plane  of  the  coil,  to  one  perpen- 
dicular to  it,  it  is  necessary  to 
turn  the  pivot,  and  therefore 
the  pointer,  through  180°;  the 
actual  working  range  of  deflec- 
tion is  about  100°.  These  in- 


FIG.  36. — Inclined-coil  ammeter.     (General  Electric  Co.) 


struments  are  now  made  with  laminated  magnetic  shields  and 
magnetic  damping. 


THE  ELECTRODYNAMOMETER  AND  THE  CURRENT  BALANCE 

The  electrodynamometer  is  distinguished  from  the  moving  coil 
galvanometer  by  having  the  movable  member  suspended,  not  in 
the  field  of  a  permanent  magnet,  but  in  that  due  to  a  system  of 
fixed  coils  which  are  traversed  by  the  current. 

Electrodynamometers  may  be  either  absolute  or  secondary 
instruments.  The  coils  may  be  arranged  in  various  ways  but  in 


THE  MEASUREMENT  OF  CURRENT 


73 


an  absolute  instrument  the  arrangement  and  proportions  must 
be  such  that  the  constant  of  the  instrument  may  be  accurately 
calculated  from  the  measured  dimensions.  The  Helmholtz  ar- 
rangement is  sometimes  adopted  for  both  the  fixed  and  movable 
members,  but  in  the  instrument  shown  in  Fig.  37,  which  was  espe- 
cially designed  for  absolute  measurements,  the  coils  are  wound 
on  cylinders. 


t 

1 

a 

1 

i 

roQOOOOOnoooon 

I          < 

"    ; 

c 
c 

FIG.  37. — Absolute  electrodynamometer. 

The  fixed  coil  of  NF  turns  consists  of  a  single  layer  of  insulated 
wire  wound  on  a  plaster  of  paris  or  marble  cylinder,  which  is  very 
accurately  turned. 

The  movable  coil  of  NM  turns  is  wound  in  a  single  layer  on  a 
carefully  ground  porcelain  cylinder.  The  coils  are  placed  con- 
centrically. The  diameter  of  the  movable  coil  is  about  one-fifth 
that  of  the  fixed  coil. 

The  movable  member  is  suspended  by  a  torsion  wire  and  the 


74  ELECTRICAL  MEASUREMENTS 

current  is  taken  to  it  by  two  mercury  cups,  the  leads  being  as 
far  as  possible  concentric,  to  avoid  disturbing  effects. 

A  torsion  head  is  used  in  reading,  so  any  effect  due  to  the  angu- 
lar displacement  of  the  axes  of  the  coils  from  the  perpendicular 
position  is  avoided.  The  suspension  wire  is  the  most  troublesome 
feature  of  the  instrument,  for  its  torsional  properties  must  be  so 
definite  that  they  can  be  determined  to  a  high  degree  of  accuracy. 
A  well-aged  phosphor-bronze  wire  is  the  most  satisfactory. 

The  force,  in  any  given  direction,  which  acts  on  a  circuit  carry- 
ing a  current  IM,  when  it  is  placed  in  a  magnetic  field,  is  equal  to 
the  product  of  the  current  and  the  space  rate  of  change  of  flux 
through  the  circuit  when  the  circuit  is  displaced  in  the  given 
direction.  If  the  flux  is  due  to  a  second  circuit,  its  value  will 
be  IFm,  where  IF  is  the  current  in  the  second  circuit  and  m  is 
the  coefficient  of  mutual  induction  of  the  two  circuits.  Conse- 
quently, the  force  in  the  direction  x  is 


Similarly,  the  turning  moment  acting  between  the  coils  of  an 
electro-dynamometer  and  tending  to  change  the  angle  6  between 
their  axes  is  given  by 

M  =  /,/„  d£  (62) 

To  use  these  relations  it  is  necessary  to  have  expressions  for  m 
in  terms  of  the  numbers  of  turns  in  the  coils,  their  dimensions, 
and  their  distance  apart;  in  general,  m  must  be  expressed  in  the 
form  of  a  series,  examples  of  which  may  be  found  in  Maxwell's 
"  Treatise  on  Electricity  and  Magnetism,"  and  in  Gray's  "  Abso- 
lute Electrical  Measurements." 

In  accordance  with  the  above,  if  a  plane  circuit  of  area  A, 
which  is  traversed  by  a  current  IM,  is  suspended  in  a  uniform  mag- 
netic field  of  strength,  H',  it  will  experience  a  turning  moment 
—  M  =  AIMH'  sin  6  where  0  is  the  angle  between  the  perpen- 
dicular to  the  coil  and  the  direction  of  the  field  H'.  This  simple 
relation  cannot  be  used  in  connection  with  the  electro-dynamom- 
eter except  as  a  first  approximation,  for  the  field  due  to  the  fixed 
coil  is  not  uniform  throughout  the  space  occupied  by  the  movable 
coil. 


THE  MEASUREMENT  OF  CURRENT  75 

In  electrodynamometers  when  used  with  direct  currents,  H' 
is  the  sum  of  the  field  due  to  the  current  circulating  in  the  fixed 
coils  which  form  a  part  of  the  instrument,  and  the  local  field. 

An  approximate  expression  for  the  turning  moment  acting 
on  the  movable  coil,  assuming  it  to  be  a  plane  circuit,  may  be 
obtained. 

Referring  to  Fig.  37,  the  field  at  the  po.'nt  0,  the  center  of  the 
fixed  coil,  may  be  obtained  as  follows:  Let  the  number  of  turns 
per  centimeter  of  length  of  the  coil  be  n  and  let  x  be  the  axial  dis- 
tance of  a  turn  from  the  center.  If  IF  is  the  current  in  the  wire, 
a  belt  of  winding  8x  cm.  long  will  produce  at  the  center  a  field 
whose  component  along  the  axis  is 


5H  =  7  ^~^: T=      ==  =  2ira2nIF  ^r 


The  effect  of  the  whole  coil  will  be 

dx 


H  = 


C+b 
I       7- 

J_  b    (d 


.       _     b      Va2  +  b2 
If  Np  is  the  total  number  of  turns 

2wNFIF 

=  v^T&' 

If  the  movable  coil  of  NM  turns  has  a  radius  r,  and  the  field  in 
which  it  is  placed  is  uniform  and  of  strength  H,  the  mutual  in- 
ductance between  the  fixed  and  movable  coils  is 


m  =      TTTM  cos      =  - 


\/a 


where  6  is  the  angle  between  the  axes  of  the  coils. 
The  turning  moment  is 

dm       2TT2r2NMlMNfIF  sin  0 

lFlM^e"          VoM^~ 

and  when  the  axes  are  perpendicular,  this  becomes 


A/a2  +  62 
As  implied  above,  the  turning  moment  due  to  the  mutual  ac- 


76  ELECTRICAL  MEASUREMENTS 

tion  of  the  two  coils  cannot  be  exactly  calculated  in  this  simple 
manner,  for  to  be  exact,  m  must  be  expressed  in  the  form  of  a  series. 
However,  in  this  particular  case,  as  pointed  out  by  A.  Gray,14 

if  the  ratio  of  the  radius  of  each  coil  to  its  length  is  — -/=  all  the 

terms  in  the  series  between  the  first  and  seventh  drop  out  and 
all  but  the  first  term  are  so  very  small  that  they  may  be 
considered  as  corrections,  to  be  calculated  if  the  accuracy  of 
the  work  demands  it. 

The  result  of  careful  analysis  shows  that  the  turning  moment 
due  to  the  mutual  action  of  the  two  coils,  if  they  are  concentric- 
ally placed  with  their  axes  perpendicular,  is  given,  to  a  very  high 
degree  of  approximation,  by 

M  =  2^2r2j^^*jg 
or  if  the  two  coils  are  in  series,  by 


,,         irFM 

M    =    --  7—  --        :  -- 

V  a2  +  b2 

Of  course  the  field  in  which  the  movable  coil  is  placed  is  not 
uniform,  but  with  coils  proportioned  as  stated  above,  the  instru- 
ment acts  as  if  a  plane  circuit  having  the  net  area  of  the  movable 
coil  were  suspended  in  a  uniform  field  of  strength, 


~~ 


62 


Secondary  Electrodynamometer.—  Siemens  Dynamometer.— 
A  form  of  secondary  electrodynamometer  in  common  use  is 
shown  in  Fig.  38.  The  fixed  coils  are  firmly  supported  from  a 
wooden  pillar  which  carries  at  its  top  a  torsion  head  provided 
with  a  pointer  which  can  be  moved  over  a  uniformly  graduated 
circle. 

The  wooden  frame  effectually  prevents  any  errors  which  might 
be  introduced  in  alternating-current  work  by  currents  induced 
in  the  supports  for  the  coils. 

The  movable  coil  hangs  freely  from  a  pivot  which  rests  in  a 
jewel  carried  by  a  stirrup  attached  to  the  graduated  plate.  The 
torsion  head  is  connected  to  the  movable  system  by  a  loosely 


THE  MEASUREMENT  OF  CURRENT 


77 


coiled  spiral  spring.  A  pointer,  which  normally  stands  at  zero, 
is  attached  to  the  movable  coil;  on  the  passage  of  the  current, 
this  pointer  deflects  against  a  stop  and  is  brought  back  to  its 
original  position  by  turning  the  torsion  head.  The  amount  of 
twist  which  it  is  necessary  to  give  the  spring  in  order  to  return 
the  coil  to  its  zero  ;j$0sition  is  read  from  the  graduated  circle. 
If  the  spring  be  perfect,  the  moment  exercised  by  it  will  be  pro- 
portional to  this  angle  of  twist.  As  springs  cannot  in  general 
be  relied  upon  throughout  the  whole  range  of  twist,  the  instru- 
ment should  be  calibrated  at  a 
number  of  points  and  a  calibration 
curve  drawn. 

The  current  is  led  into  the  mov- 
able coil  by  two  stout  wires  which 
dip  into  mercury  cups. 

Setting  up  the  Siemens  Elec- 
trodynamometer. — The  instrument 
must  be  levelled  and  the  same  rela- 
tive position  of  the  coils  maintained 
during  calibration  and  subsequent 
use.  Though  the  instrument  is  to 
be  used  with  alternating  currents, 
it  is  convenient  to  employ  direct 
currents  in  the  calibration.  If  this 
is  done  it  is  desirable  to  place  the 
instrument  so  that  the  local  field 

will  have  no  influence.  This  may  be  accomplished  by  turning 
the  dynamometer  in  azimuth  until  a  position  is  found  where  the 
strongest  current  which  is  to  be  used  produces  no  deflection 
when  sent  through  the  movable  coil  alone. 

The  Law  of  the  Electrodynamometer. — The  law  of  the  electro- 
dynamometer  is  dependent  on  the  method  of  reading.  Two 
cases  will  be  considered: 

1.  When  the  movable  coil  is  always  brought  back  to  its  initial 
position  by  the  use  of  a  torsion  head,  as  in  the  Siemens  instrument. 

2.  When  the  movable  coil  is  allowed  to  deflect,  as  in  an  ordinary 
reflecting  galvanometer. 

1.  When  an  electrodynamometer,  set  up  without  regard  to  the 
local  field,  is  used  with  direct  currents,  a  part  of  the  turning 


FIG.  38. — Siemens  electro- 
dynamometer. 


78  ELECTRICAL  MEASUREMENTS 

moment  is  due  to  the  action  of  that  field  on  the  movable  system. 
This  will  be  proportional  to  the  current  through  the  movable 
coil.  The  field  due  to  the  fixed  coil  is  proportional  to  the  current 
through  it,  so  the  total  turning  moment  will  be  M  =  KiIFIM  ± 
K2HIM.  If  the  coils  are  in  series,  the  moment  corresponding  to 
a  current  7,  will  be 

M  =  KJ*  ±  K2HL 

KI  is  a  factor  which  depends  on  the  dimensions  and  the  numbers 
of  turns  of  both  coils,  and  on  the  angle  between  their  axes.  Kz 
depends  on  the  dimensions  and  number  of  turns  of  the  movable 
coil  and  on  the  position  of  the  coil  in  the  local  field,  H. 

To  eliminate  the  effect  of  the  local  field  two  readings  may  be 
taken,  the  current  being  reversed.  In  each  case  the  torsion 
head  is  adjusted  until  the  original  relative  position  of  the  coils 
is  reproduced.  Then,  if  r  is  the  torsion  constant  of  the 
controlling  spring  and  6  is  the  twist  in  the  spring, 

M,  =  K,P  +  K2HI  =  rBl 
M2  =  KJ2  -  K2HI  =  r62 
or 


If  an  alternating  or  regularly  pulsating  current  is  employed, 
the  turning  moment  passes  through  a  cycle  of  values  with  each 
complete  period.  As  the  natural  time  of  vibration  of  the  movable 
system  is  much  greater  than  the  period  of  the  current,  the  system 
will  take  up  a  position  dependent  upon  the  average  turning 
moment,  that  is,  the  twist  in  the  controlling  spring  will  be  given 

by 


I     If 

'     U 


The  subscripts  F  and  M  refer  to  the  fixed  and  movable  coils 
respectively.     T  is  the  time  of  a  complete  cycle. 
With  alternating  currents  this  becomes 

K    1  CT 
&  =  - --  7p  I    ifindt 

r     IJo 

that  is,  the  deflection  when  a  torsion  head  is  used,  is  proportional 


THE  MEASUREMENT  OF  CURRENT  79 

to  the  mean  product  of  the  currents  in  the  two  coils.  Therefore, 
if  the  coils  are  in  series  the  deflection  is  proportional  to  the  mean 
square  of  the  current  or  to  the  square  of  the  effective  value. 
The  currents  in  the  two  coils  may  differ  in  wave  form  and  in  time 
phase  as  well  as  in  magnitude.  For  instance,  expressing  both  iF 
and  IM  in  the  form  of  a  series,  if  the  waves  are  non-sinusoidal, 


=  Ai  sin  cot  -f  A  2  sin  (2co£  —  <p2)  +  A3  sin 
=  BI  sin  (ut  —  <p'i)  +  B2  sin  (2ut  —  <p'2)  + 

B3  sin 


It  is  well  known  that  the  mean  product  of  two  sine  curves 
which  differ  in  periodicity  is  zero,  and  that  the  mean  product  of 

two  sine  curves  of  the  same  periodicity  is  -^  cos  a  where  /i  and 

£t 

7  2  are  the  maximum  values  and  a  is  the  angle  of  phase  difference. 
Consequently, 


BT  1  I     •  •    j,        TS  [AiBi          ,  ,  . 

r0  =  A.iy  I    IFIM  at  =  Ki^    ^     cos  <p  i  +  T-g—  cos  (tpz  —  <p  2) 

—  |-^  cos  (<^3  -  <p'a)  +    .    .    .  J   (63) 

If  the  fixed  and  movable  coils  are  in  series,  as  they  are  when 
currents  are  measured,  An  =  Bn  =  In  and  cos  (<pn  —  <p'n)  =  1,  so 

re  =  K  i*dt  =  K-    +        +        +...=  KJ*    (64) 


/i,  J2,  Is,  etc.,  are  the  maximum  values  of  the  various  compo- 

/i2 

nents.    -^-  is  the  square  of  the  effective  value  of  the  fundamental, 

/22 

-7T-  is  the  square  of  the  effective  value  of  the  second  harmonic, 

Zi 

etc.,  and  I2  is  the  square  of  the  effective  value  of  the  current. 

2.  When  the  movable  coil  is  allowed  to  deflect,  the  factor  K\  be- 
comes a  variable  depending  on  the  angle  between  the  axes  of  the 
fixed  and  movable  coils.  If  the  field  due  to  the  fixed  coil  is  uni- 
form or,  what  practically  amounts  to  the  same  thing,  if  the  mov- 
able coil  is  very  much  smaller  than  the  fixed  coil,  K\  is  propor- 
tional to  the  cosine  of  the  angle  of  displacement  of  the  axes  of  the 


80 


ELECTRICAL  MEASUREMENTS 


coils  from  a  perpendicular  position.     However,  Lord  Rayleigh* 
has  called  attention  to  the  fact  that  the  mutual  inductance  of 


two  concentric  circles,  the  ratio  of  whose  radii  is 


=  0.548, 


is,  over  a  considerable  range,  very  nearly  proportional  to  the 
angular  displacement  of  the  axes  from  the  perpendicular  position. 


g 

5 

/ 

^- 

S 

4 

/ 

/ 

*^s 

/ 

> 
1 

/ 

rt 
1 

1     / 

/ 

/ 

90°  8 

0°70°( 

0U50°4 

0°30°2 

0°1<// 

10°20°30°4 
Angular  Di& 

b°50060070080°900 
placement  of  Axes 

/ 

/ 

o 

/ 

/ 

A 

/ 

/ 

^ 

/ 

a 

FIG.  39. — Showing  relation  between  the  mutual  inductance  of  two  circles 
and  the  angular  displacement  of  their  axes  from  the  perpendicular  position 
when  the  ratio  of  the  radii  is  0.548. 

This  is  illustrated  by  Fig.  39  in  which  relative  values  of  the  mutual 
inductance  are  plotted  against  the  angular  displacements  of  the 
axes  of  the  coils  from  the  perpendicular  position. 

From  the  figure  it  is  seen  that  over  a  wide  range  -rr  is  practi- 

CtU 

cally  constant.     As  the  turning  moment  due  to  the  mutual  action 

*"The  Inductance  and  Resistance  of  Compound  Conductors,"   (Phil. 
Mag.,  December,  1886,  p.  470). 


THE  MEASUREMENT  OF  CURRENT  81 

of  two  coils  is  IFIM^TQ  the  deflection  of  an  electrodynamometer 

with  coils  of  small  cross-section  thus  proportioned,  neglecting  the 
action  of  local  fields,  should  be  very  nearly  proportional  to  the 
square  of  the  current.  Also,  if  the  coils  of  a  deflectional  watt- 
meter (page  306)  be  thus  proportioned,  the  scale  should  be  sen- 
sibly uniform  throughout  the  working  range  of  the  instrument. 

If  the  movable  coil  of  a  sensitive  dynamometer,  designed  as 
just  suggested,  is  allowed  to  deflect  and  the  angular  movement 
is  read  by  the  mirror  and  scale  method,  in  general,  when  direct 
currents  are  used  the  conditions  are  as  indicated  by  Fig.  40. 


FIG.  40. — Pertaining  to  effect  of  local  field  on  a  deflectional 
electrodynamometer. 

If  A  is  the  equivalent  area  of  the  movable  coil,  H  the  strength 
of  the  local  field,  and  6  the  deflection, 

T0i  =  KJFIM  +  IMAH  sin  (a  +  0  -  0i). 

If  both  currents  are  reversed  the  sign  of  the  term  involving  H 
will  be  changed, 

T02  =  KJFIM  ~  IMAH  sin  (a  +  /3  -  02). 

In  setting  up  the  instrument  0  is  made  as  near  0°  and  a  as 
near  90°  as  possible,  then 

r0!  =  KJPIM  +  IMAH(cos  00 
and  if  the  coils  are  in  series 

r,0  =  KJ*  +  I  AH  cos  0L 
If  the  instrument  is  read  by  telescope  and  scale  the  angle  of 


82 


ELECTRICAL  MEASUREMENTS 


deflection  is  small  and  cos  0  is  practically  unity.     If  D  represents 
the  scale  reading  then,  nearly  enough, 

n  TTr   T2     I      iff   T 

JL>i  —  K  \L*  +  K  21 
and  on  reversing  the  current 


where  K'i  and  K'z  are  con- 
stants. /  is  the  numerical 
value  of  the  current  without 
regard  to  sign.  The  law  of  a 
sensitive  electrodynamometer 
when  used  with  direct  currents 
is  shown  in  Fig.  42.  The  in- 
strument was  adjusted  so  that 
initially  the  axes  of  the  coils 
were  perpendicular,  with  the 
axis  of  the  fixed  coil  coincid- 
ing in  direction  with  the  local 
field. 

To  make  this  adjustment 
an  alternating  current  may 
be  sent  through  the  fixed  coil, 
the  circuit  of  the  movable  coil 
being  closed  through  a  tele- 
phone. The  desired  position 
is  attained  when  the  mutual 
inductance  is  zero,  that  is, 
when  the  telephone  is  silent. 
This  adjustment  having  been 
made,  the  axis  of  the  fixed 
coil  may  be  made  to  coincide 
with  the  local  field  if  a  direct  current  be  sent  through  the  mov- 
able coil  alone  and  the  instrument  turned  in  azimuth  until  the 
deflections  with  reversed  currents  are  equal. 

Referring  to  Fig.  42  and  employing  10~3  amp.  as  the  unit  of 
current,  for  this  particular  instrument, 

Di  =  25.8P  +  18.37 
D2  =  25.8I2  -  18.3/ 


FIG.  41. — Sensitive  electrodyna- 
mometer. 


THE  MEASUREMENT  OF  CURRENT 


83 


When  alternating  currents  are  used,  the  term  due  to  the  local 
field  is  absent,  consequently  the  calibration  curve  will  be  obtained 

by  plotting  a  new  curve,  the  abscissae  being  D  =  -         —  •     For 

2i 

this  case  D  =  25. 8/2.     The  new  curve  is  shown  by  the  dotted 
line  in  Fig.  42. 

It  is  to  be  noted  that  a  high  sensitivity  is  obtained  by  having 
many  turns  on  the  coils.  At  high  periodicities,  therefore,  both 
the  resistance  and  reactance  of  the  coils  conspire  to  alter  the 
circuit  conditions  when  the  instrument  is  introduced. 


CALIBRATION  CURVES  FOR  SENSITIVE 

ELECTRODYNAMOMETER 
*  /-With  Direct  Current 
#77-  With  Alternating  Current 
Currents  are  in  Milliamperes 


28    30    32   34   36 


FIG.  42. — Calibration  curves  for  sensitive  electrodynamometer. 

Astatic  Electrodynamometers. — All  troubles  due  to  uniform 
local  and  stray  fields  may  be  obviated  by  making  the  instrument 
astatic.  Fig.  43  shows  a  simple  arrangement  of  this  sort. 

The  current  circulates  in  opposite  directions  in  the  two  rigidly 
connected  movable  coils  which  are  identical  in  dimensions  and 
numbers  of  turns  and  are  connected  in  series;  hence,  the  movable 
system  when  traversed  by  direct  currents  will  experience  no 
turning  moment  due  to  the  earth's  field.  Again,  stray  fields  due 
to  either  direct  or  alternating  currents  have  no  effect  provided 
they  are  sufficiently  uniform  so  that  the  strength  is  the  same 
at  both  the  upper  and  lower  coils.  The  two  sets  of  fixed  coils 
are  so  connected  that  they  both  tend  to  turn  the  movable  member 
in  the  same  direction. 


84 


ELECTRICAL  MEASUREMENTS 


An  astatic  instrument  can  be  set  up  without  regard  to  the 
earth's  field  and  calibrated  with  direct  currents.  The  curves  so 
obtained  are  immediately  applicable  to  either  direct-  or  alter- 
nating-current measurements. 

In  the  instrument  shown  in 
Fig.  43,  the  damping  is  ob- 
tained by  means  of  mica 
vanes  moving  in  the  closed 
chamber  at  the  base  of  the 
instrument. 

The  Irwin  Astatic  Electro - 
dynamometer. — The  Irwin 
astatic  instrument  is  inter- 
mediate between  the  electro- 
dynamometer  and  the  current 
balance.  The  fixed  turns  are 
in  the  form  of  two  coaxial 
circular  coils  of  the  same  di- 
ameter, through  which  the 
current  circulates  in  opposite 
directions,  thus  producing  be- 
tween the  faces  of  the  coils  a 
field  which  is  directed  radially 
outward.  The  movable  mem- 
ber consists  of  two  semicir- 
cular coils  mounted  on  a  thin 
disc  of  mica,  the  directions 
of  the  currents  being  as  in- 
dicated. The  straight  sides 
are  as  nearly  as  possible  in 
the  axis  of  rotation,  the 
G-urved  sides  move  in  the  field 
between  the  two  fixed  coils, 
being  attracted  by  one  and 
repelled  by  the  other.  This 
construction  brings  the  two  movable  coils  very  near  together, 
which  is  advantageous  as  it  reduces  any  effect  which  may  be 
due  to  non-uniformity  of  the  local  or  stray  field. 


FIG.  43. — Astatic  electrodyna- 
mometer. 


THE  MEASUREMENT  OF  CURRENT 


85 


Rewinding  an  Electrodynamometer  to  Obtain  a  Given  Per- 
formance.— As  the  deflection  of  an  electrodynamometer  when 
used  with  alternating  currents  is  proportional  to  the  square  of 
the  current,  the  range  of  the  instrument  is  limited.  It  is  desirable, 
therefore,  to  have  the  fixed  coil  subdivided  by  taps  so  that  the 
number  of  turns  may  be  varied. 

It  is  sometimes  necessary  to  alter  the  sensitivity  of  secondary 
dynamometers  so  that  definite  deflections  may  be  obtained  with 
stated  currents.  If  the  corresponding  dimensions  of  the  coils  of 
the  original  and  the  rewound  instruments  are  the  same,  the  calcu- 


FIG.  44. — Irwin  astatic  electrodynamometer. 

lation  of  the  proper  number  of  turns  is  simply  a  matter  of  pro- 
portion, provided  one  has  data  concerning  the  number  of  turns 
on  the  coils  and  the  performance  of  the  original  instrument.  If 
the  instrument  is  properly  set  up, 

rd  =  KFMP  (65) 

F  and  M  are  the  numbers  of  turns  on  the  fixed  and  movable  coils 
respectively,  and  K  is  a  constant  depending  upon  the  geometry 
of  the  coil  system.  This  may  be  determined  from  a  knowledge 
of  the  torsion  constant  of  the  spring,  the  number  of  fixed  and 
moving  turns  on  the  original  instrument  and  the  deflection  corre- 
sponding to  a  given  current.  After  K  has  been  found,  the  value 


86  ELECTRICAL  MEASUREMENTS 

of  FM,  the  required  product  of  the  fixed  and  moving  turns  for  the 
new  winding,  is  readily  determined. 

Electrodynamometers  for  Heavy  Currents. — For  several 
reasons  it  is  difficult  to  apply  the  ordinary  electrodynamometer 
to  the  measurement  of  very  large  currents.  If  the  coils  are  used 
in  series,  trouble  is  experienced  in  getting  the  current  into  and  out 
of  the  movable  member.  Where  any  considerable  current  is  to 
be  carried,  the  necessary  flexible  connections  are  made  by  means 
of  mercury  cups,  and  no  dynamometer  in  which  they  are  em- 
ployed can  be  considered  a  portable  instrument  as  that  term  is 
now  generally  understood.  There  are  also  the  structural  diffi- 
culties due  to  the  necessity  of  supporting  a  heavy  movable  coil 
on  pivots  which  are  practically  free  from  friction  and  are  suffi- 
ciently strong  so  that  the  instrument  will  stand  handling.  These 
considerations  preclude  the  use  of  the  electrodynamometer  with 
its  coils  in  series  as  an  alternating-current  ammeter,  and  are 

the  reasons  for  the  survival  of  soft  iron 
ammeters  as  alternating-current  in- 
struments. 

Again,  it  is  essential  that  the  field  at 

the   movable   coil   be   the   same   with 

FIG.      45. — Wattmeter          ,        .  . 

method  for  measuring  large  both  direct  and  alternating  currents, 
alternating  currents.  for  direct  currents  will  be  used  in  cali- 

brating and  alternating  currents  in  the 

subsequent  use  of  the  instrument.  This  equality  of  fields  may  be 
attained  either  by  arranging  the  metal  of  the  coil  so  that  the 
current  distribution  will  be  the  same  in  both  cases,  or  by  adopt- 
ing an  arrangement  which  from  its  symmetry  is  such  that  the 
change  in  distribution  in  passing  from  direct  to  alternating  cur- 
rent does  not  affect  the  field  in  which  the  movable  coil  swings. 

It  is  also  necessary  that  there  be  no  error  due  to  eddy  currents 
induced  in  the  mass  of  the  coils,  or  in  the  frames  by  which  they 
are  supported.  For  this  reason,  in  instruments  of  moderate 
capacity  recourse  is  had  to  stranding  the  conductors.  This  must 
be  very  carefully  done  so  that  all  the  strands  will  have  the  same 
effective  inductance  and  resistance  and  the  same  increase  of 
resistance  due  to  heating. 

Wattmeter  Method  for  Measuring  Large  Alternating  Currents. 
—To  obviate  the  necessity  of  taking  a  large  current  into  the 


THE  MEASUREMENT  OF  CURRENT 


87 


movable  coil,  recourse  has  been  had  in  investigation  and  calibra- 
tion work,  to  a  wattmeter  method  as  indicated  in  Fig.  45. 

The  current  coil  of  the  wattmeter  and  a  known  resistance  R  are 
inserted  in  the  circuit;  the  connections  are  such  that  the  I2R 


n 


Outer  Tube 


Mirror 
Damping  Vanex      i\J     /Wooden  Damping  Box 

n-i 


Current 
Terminal 


Inside  Tube,  Water  Cooled' 


--Moving  Coil 


roove  for  Equalizing 
Stream  Lines 


Damping  Vane 


-\    .  /-,,  Wooden  Support  for 

Adjusting  Clamps  Telescope  ^  Scale 


Cuirent  Terminal 


Wooden  Damping 

Bos. 
"Suspension 

Wooden  Support 
for  Telescope  and  Seal 

Wooden  Support-* 


FIG.  46. — Agnew  tubular  electrodynamometer. 

loss   in   the  constant  resistance,  R,  is  measured,  and  thus  the 
current  is  determined. 

Agnew  Tubular  ^Electrodynamometer.15 — This  instrument   is 
primarily  designed  for  measuring  very  large  alternating  cur- 


88  ELECTRICAL  MEASUREMENTS 

rents,  up  to  5,000  amp.,  by  the  wattmeter  method.  It  can,  of 
course,  be  used  as  an  ordinary  wattmeter  for  power  measure- 
ments. Its  distinctive  feature  is  the  means  taken  to  avoid  errors 
due  to  the  skin  effect  in  the  very  massive  conductors  which  must 
be  used  for  the  current  coil. 

As  seen  from  Fig.  46  the  current  "coil"  is  made  in  the  form 
of  two  coaxial  tubes.  When  they  are  traversed  by  the  current  a 
strong  field  will  exist  in  the  space  between  them,  while  the  field 
external  to  the  tubes  will  be  nil.  Stray-field  effects  due  to  the 
heavy  current  in  the  instrument  are  thus  avoided. 

The  movable  system  consists  of  two  rigidly  connected  coils 
one  above,  the  other  below  the  central  tube.  The  working 
position  of  the  movable  system  is  approximately  90°  from  that 
shown  in  Fig.  46.  As  the  movement  takes  place  in  a  strong  field, 
it  is  essential  that  the  movable  system  be  entirely  free  from  mag- 
netic impurities.  If  this  is  not  the  case,  the  zeroes  with  the  cur- 
rent on  and  with  the  current  off  will  not  coincide. 

The  suspension  strip  is  of  phosphor-bronze  and  air  damping  is 
provided.  Diaphragms  between  the  tubes  are  necessary  to 
prevent  disturbance  of  the  movable  system  by  air  currents. 

Theory  of  the  Tubular  Electrodynamometer.  —  Suppose  that 
two  coaxial  circular  tubes  are  arranged  as  shown  in  Fig.  47, 
the  directions  of  the  current  being  as  indicated.  Consider  any 
point,  P,  in  the  space  between  the  tubes  and  distant  r  from  the 
axis.  A  direct  current  will  distribute  itself  uniformly  over  the 
cross-section  of  the  tubes.  The  work  done  in  taking  a  unit  pole 
around  the  indicated  path  is 


where  I  is  the  current  encircled  by  the  path,  that  is,  the  current 
which  flows  in  the  central  tube,  and  H  is  the  field  strength  at 
any  and  all  points  in  the  path.  Therefore, 

H  =  - 

r 

It  is  obvious  that  this  relation  will  hold  as  long  as  a  symmetrical 
arrangement  of  the  current  around  the  central  axis  is  preserved. 
It  is  thus  evident  that  the  generating  lines  of  the  surfaces  of  the 
coaxial  tubes  need  not  be  straight  but  may  have  any  form  what- 


THE  MEASUREMENT  OF  CURRENT  89 

soever.  Symmetry  is  the  all-important  thing.  It  is  also  appar- 
ent that  any  symmetrical  redistribution  of  the  current  in  the 
conductors  will  not  alter  H. 

If  an  alternating  be  substituted  for  a  direct  current,  the  dis- 
tribution of  the  current  over  the  cross-section  of  the  tubes  will  be 
altered,  due  to  the  skin  effect,  but  from  the  symmetry  of  the 
conductors  the  new  distribution  of  the  current  will  be  symmetrical 
about  the  axis  and  therefore  the  field  due  to  the  changed  distribu- 
tion of  the  current  is  the  same  as  before. 

In  the  actual  instrument,  owing  to  the  manner  of  taking  the 
current  into  the  large  outside  tube,  the  natural  distribution  will 
not  be  quite  uniform.  For  this  reason,  a  groove  about  5  cm.  wide 
is  turned  eccentrically  in  the  tube.  By  filing,  the  groove  may 
be  so  adjusted  that  the  stream  lines  are  uniformly  distributed. 


FIG.  47. — Pertaining  to  the  Agnew  tubular  electrodynamometer. 

It  is  essential  that  the  symmetrical  distribution  of  currents 
about  the  axis  be  maintained;  therefore,  any  springing  of  the 
slender  inner  tube  must  be  avoided.  A  test  for  distribution 
errors  may  be  made  by  the  method  described  on  page  316. 

The  principal  dimensions  of  the  instrument,  as  used  at  the 
Bureau  of  Standards,  are 

Outer  tube,  length,  101  cm.;  radii,  6.41  and  7.07  cm. 

Inner  tube,  length,  125  cm.;  radii,  0.50  and  1.27  cm. 

Current  capacity,  air-cooled,  1,200  amp.,  (water-cooled)  5,000  amp. 

Field  at  center  of  movable  coils  at  full  load,  300  gausses. 

Movable  coils,  116  turns  of  0.2-mm.  silver  wire,  diameters  2.5  and  5.0 
cm.,  weight  of  each  coil  7.3  gm.;  total  resistance  of  movable  coil  circuit 
14.3  ohms;  current  capacity  0.06  amp.;  inductance  1.4  millihenries. 

Sensitiveness,  100-cm.  deflection  at  86-cm.  scale  distance  requires  100  amp. 
in  tubes  and  0.06  amp.  in  movable  coils. 

The  Current  Balance. — In  this  class  of  instruments  the  current 
is  measured  by  weighing,  with  a  gravity  balance,  the  pull  exerted 


90 


ELECTRICAL  MEASUREMENTS 


by  a  coil  upon  another  placed  in  a  parallel  plane,  their  axes  being 
coincident. 

An  absolute  current  balance  of  this  sort  was  used  by  Lord 
Rayleigh  and  Mrs.  Sidgwick,  1884,  in  their  determination  of  the 
electrochemical  equivalent  of  silver.  Since  that  time  the  instru- 
ment has  been  brought  to  a  very  high  degree  of  perfection,  par- 


FIG.  48.— Absolute  current  balance  used  at  Bureau  of  Standards  by  Rosa, 
Dorsey  and  Miller. 

ticularly  through  the  work  of  Ayrton,  Mather  and  Smith  at  the 
National  Physical  Laboratory  in  England  and  of  Rosa,  Dorsey 
and  Miller  at  the  Bureau  of  Standards  at  Washington,  D.  C.1 ; 

Rayleigh,  and  following  him,  Rosa,  Dorsey  and  Miller  used  a 
balance  with  two  equal  fixed  coils,  the  smaller  movable  coil  being 
placed  midway  between  them,  all  three  coils  being  coaxial. 

The  Rayleigh  current  balance  is  not  intended  for  general  use 
as  a  current-measuring  device,  but  for  the  absolute  measurement 


THE  MEASUREMENT  OF  CURRENT      91 

of  currents  in  special  investigations  such  as  are  necessary  in  the 
determination  of  electrical  standards  it  is  of  great  service,  and  is 
generally  considered  to  be  the  most  accurate  device  which  has 
been  developed  for  the  purpose.  Its  advantages  are: 

1.  The  constant  of  the  instrument  depends  principally  upon 
the  ratio  of  the  effective  radii  of  the  coils.     This  number  can  be 
determined  experimentally  to  a  high  degree  of  accuracy,  by  a 
method  originally  due  to  Bosscha;  the  difficulties  met  with  in 
determining  the  mean  radii  of  multiple-layer  coils  from  mechan- 
ical measurements  are  thus  avoided.     This  is  the  peculiar  ad- 
vantage of  the  Rayleigh  form  of  balance. 

2.  The  measurements  are  independent  of  the  local  field  and 
its  variations. 

3.  The  determination  of  torsion  constants  is  entirely  avoided. 

4.  Analysis  shows  that  when  the  distance  between  the  fixed 
and  movable  coils  is  equal  to  one-half  the  radius  of  the  larger 
coil,  slight  inaccuracies  in  the  placing  of  the  movable  coil  produce 
very  small  errors  in  the  calculated  constant  of  the  instrument. 

Fig.  48  shows  the  current  balance  used  by  Rosa,  Dorsey  and 
Miller,  together  with  an  enlarged  iview  of  the  coil  system.  The 
two  fixed  coils  have  a  radius  of  50  cm.  and  are  placed  25  cm. 
apart.  They  are  wound  on  brass  frames,  the  material  for  which 
was  carefully  selected,  for  even  good  brass  is  slightly  magnetic. 
Enamelled  wire  was  used.  The  movable  coil,  25  cm.  in  diameter, 
is  hung  from  a  precision  balance  and  the  force  determined  by  the 
change  in  weight  necessary  to  restore  the  balance  to  equilibrium 
when  the  current  in  the  fixed  coil  is  reversed.  This  change  was 
6  gm.  To  prevent  disturbance  of  the  balance  by  air  currents 
set  up  by  the  heating  of  the  coils,  the  fixed  coils  are  water- 
cooled  and  the  movable  coil  is  hung  in  a  water-jacketed  cham- 
ber which  is  kept  at  a  constant  temperature. 

When  the  balance  is  used  in  the  manner  indicated, 

I*K  =  Ml' 
2 

M  is  the  change  in  the  weights,  corrected  for  buoyancy  of 
the  air,  which  is  necessary  to  restore  the  balance  to  equilibrium 
when  the  current  in  the  fixed  coil  is  reversed,  and  g  is  the  accelera- 
tion due  to  gravity. 


92  ELECTRICAL  MEASUREMENTS 

The  factor  K  depends  principally  on  the  ratio  of  the  radii  of 
the  fixed  and  movable  coils.  It  is  equal  to  -5—  where  ra  is  the 

mutual  inductance  of  the  coils  and  dx  refers  to  an  axial  displace- 
ment of  the  movable  coil,  ra  can  be  calculated,  in  the  form  of  a 
series,  from  the  numbers  of  turns  and  the  dimensions  of  the  coils. 

Secondary  Current  Balances. — The  Kelvin  Balance. — In  the 
Kelvin  balance  there  are  four  fixed  and  two  movable  coils,  the 
latter  being  carried  at  the  ends  of  a  balance  arm  which  turns 
about  a  horizontal  axis,  see  Fig.  49.  Each  movable  coil  is  situ- 
ated between  two  fixed  coils  and  all  six  coils  are  connected  in 
series.  In  place  of  a  knife  edge,  the  beam  is  suspended  by  a  large 
number  of  filaments  of  copper  wire,  forming  a  sort  of  stranded  rib- 
bon, which  provides  a  ready  means  for  making  the  electrical  con- 
nection to  the  movable  coil.  Absence  of  friction,  large  radiating 
surface,  and  cooling  by  conduction  to  the  frame  are  the  advan- 
tages attained  by  this  means. 

The  center  of  gravity  of  the  movable  system  may  be  adjusted 
as  in  an  ordinary  balance,  by  means  of  a  weight  on  a  short  verti- 
cal rod  immediately  above  the  point  of  support. 

The  bobbins  and  the  base  plate  are  made  of  slate,  thus  insuring 
rigidity  and  absence  of  eddy  currents.  Means  for  levelling  the 
instrument  and  for  removing  the  weight  of  the  movable  parts 
from  the  suspension  wires  when  the  instrument  is  not  in  use  are 
provided. 

A  uniformly  graduated  bar  is  attached  to  the  movable  system 
and  is  supplied  with  a  sliding  carriage  upon  which  the  weights 
can  be  placed  in  a  definite  position,  small  conical  pins  on  the 
carriage  fitting  into  corresponding  holes  in  the  weights.  The 
carriage  can  be  manipulated  from  without  the  case  by  means  of 
cords  attached  to  a  self-releasing  pendent,  which  slides  on  guides 
attached  to  the  base  of  the  instrument. 

The  zero  of  the  graduated  bar  is  at  the  extreme  left  hand.  If, 
when  no  current  is  flowing  in  the  balance,  the  sliding  weight  is 
set  at  zero  and  the  corresponding  counterpoise  placed  in  the  V-- 
shaped trough  attached  to  the  right-hand  movable  coil,  then  the 
pointer  attached  to  the  beam  should  stand  at  a  reference  mark 
upon  the  short  vertical  scale  attached  to  the  base  of  the  instru- 
ment. If  this  is  not  so,  a  means  of  adjustment  is  provided  in  a 


THE  MEASUREMENT  OF  CURRENT 


93 


small  metal  flag  attached  to  the  movable  system  which  can  be 
manipulated  by  means  of  a  forked  lever  operated  from  outside 
the  case. 

Suppose  that  the  movable  weight  is  set  at  zero  and  that  the 
balance  is  in  equilibrium  when  no  current  is  passing.  On  the 
passage  of  the  current  the  equilibrium  will  be  upset  and  the  right- 


FIG.  49. — Kelvin  current  balance. 

hand  end  of  the  beam  will  rise.  To  restore  the  equilibrium  it  is 
necessary  to  increase  the  turning  moment  due  to  the  weights. 
This  is  accomplished  by  displacing  the  movable  weight  toward 
the  right.  The  change  in  the  total  moment  due  to  the  weights  is 
proportional  to  the  displacement  of  the  movable  weight  from  its 
zero  position,  and  this  must  be  equal  to  the  moment  due  to  the 


94  ELECTRICAL  MEASUREMENTS 

action  of  the  coils,  which  is  proportional  to  the  square  of  the 
current. 

The  device  of  using  the  weight  in  two  portions  is  adopted 
because  the  beam  can  then  be  made  twice  as  long  as  would  other- 
wise be  the  case. 

The  current  is  calculated  by  the  formula  I  =  K  2\/R,  where 
R  is  the  displacement  of  the  weight  as  read  on  the  uniformly 
graduated  scale.  A  table  of  doubled  square  roots,  supplied 
by  the  maker,  is  of  service  in  the  calculation. 

For  rough  work,  the  position  of  the  sliding  weight  may  be 
referred  to  the  fixed  inspectional  scale,  placed  immediately 
behind  the  scale  beam.  It  is  graduated  to  give  the  qu'antity 
2\/R  directly.  For  the  purpose  of  extending  the  range  four  sets 
of  weights  are  supplied  with  each  instrument. 

The  Kelvin  balances  are  made  in  a  variety  of  ranges  up  to 
2,500  amp.  Their  particular  field  of  usefulness  is  as  secondary 
standards  in  the  calibration  of  alternating-current  ammeters. 
They  are  serviceable  in  laboratories  where  the  circuit  conditions 
can  be  controlled,  but  are  not  adapted  to  the  measurement  of 
fluctuating  currents. 

MEASUREMENT     OF     CURRENTS     IN     PERMANENTLY     CLOSED 

CIRCUITS17 

Occasionally  it  is  necessary  to  measure  the  current  in  a  con- 
ductor which  cannot  be  broken  to  allow  the  introduction  of  an 
ammeter  or  shunt.  For  example,  such  cases  occur  in  the  investi- 
gation of  the  electrolytic  deterioration  of  underground  pipes  for 
water  or  gas,  due,  for  instance,  to  the  stray  currents  caused  by 
the  use  of  a  ground  return,  or  imperfect  bonding,  in  a  traction 
system.  The  damage  occurs  where  the  current  leaves  the  pipe, 
and  may  cause  such  a  menace  to  health  and  property  that  large 
expenditures  of  time  and  money  are  justifiable  in  locating  the 
source  of  the  trouble  and  in  its  elimination. 

In  this  or  similar  cases,  if  the  resistance  between  two  potential 
points  on  the  pipe  or  other  conductor  can  be  determined,  the 
current  may  be  measured  by  using  this  resistance  as  a  shunt,  a 
millivoltmeter  being  used  to  determine  the  P.D.  between  the 
points.  The  problem  thus  resolves  itself  into  the  determination 


THE  MEASUREMENT  OF  CURRENT      95 

of  the  resistance  of  a  portion  of  a  conductor  which  may  be  carry- 
ing a  current  and  which  must  be  measured  in  situ  without  being 
opened. 

Suppose  that,  as  a  preliminary  to  measuring  the  stray  current 
in,  for  instance,  a  water  main,  it  is  necessary  to  determine  the 
resistance  between  two  plugs  which  have  been  screwed  into 
the  pipe  to  serve  as  potential  terminals. 

The  pipe  is  supposed  to  be  traversed  by  stray  currents  of  un- 
known strength.  The  necessary  connections  are  shown  in  Fig. 
50.  At  Vi  and  V2  are  2  millivoltmeters,  with,  perhaps,  10  milli- 
volt scales;  they  are  connected  to  potential  points  at  b,  c  and  e,  f. 
These  points  are  obtained  by  drilling  into  the  pipe  and  firmly 
inserting  brass  plugs  to  which  the  leads  may  be  soldered.  It  is 


FIG.  50. — Connection  for  measuring  a  direct  current  without  opening 

the  circuit. 

essential  that  the  instruments  be  calibrated  with  the  leads  which 
are  to  be  used  in  the  test.  At  B  is  a  storage  battery  capable  of 
yielding  enough  current  to  give  a  good  reading  on  V\  (100  or 
200  amperes  for  a  15-in.  iron  pipe),  at  A  is  the  ammeter  by 
which  the  current  from  B  is  measured,  and  K  is  the  switch  by 
which  the  current  is  controlled. 

The  spacing  of  the  points  a,  b,  c,  d  is  important,  for  the  four 
points  b,  c,  e,  f  should  be  on  four  equipotential  planes  through  the 
pipe.  Therefore  the  distance  between  a  and  b  and  between  c  and 
d  should  be  great  enough  so  that  the  current  from  B  may  spread 
out  and  the  stream  lines  become  uniformly  distributed  before  the 
points  c  and  b  are  reached;  the  lengths  of  ab  and  cd  should  be 
about  twice  the  diameter  of  the  pipe,  the  points  a  and  d  being  on 
the  top  and  b  and  c  on  the  side. 

The  positive  direction  of  the  currents  may  be  assumed  as 
indicated;  it  is  essential  that  such  an  assumption  be  made  at  the 


96  ELECTRICAL  MEASUREMENTS 

start,  otherwise  confusion  may  arise  and  the  results  be  of  no 
value. 

The  procedure  is  as  follows:  Observe,  if  necessary,  the  tem- 
perature of  the  conductor.  With  K  open,  simultaneous  readings 
of  the  millivoltmeters  are  taken.  Denote  them  by  Vi  and  F2, 
then 

'T*  ~\7 


K  is  then  closed  and  simultaneous  readings  of  the  ammeter  and  of 
the  two  millivoltmeters  are  taken.  Call  the  readings  7,  V\,  V2, 
and  denote  the  stray  current  in  the  pipe  at  the  instant  of  reading 
by  Is.  Then  the  current  across  x,  at  that  instant,  will  be 

/„=-/  +  /. 

also 

Ixx  =  V\ 


From  these 


r\  =  -  Ix  +  Isx  =  - 
=  ~  Vr    +  Vf 


I          IV, 
and 

V*Vi'       V'<L 

r  —    —  __L  _|_         -. 

FJ          7 

The  test  should  be  repeated  with  the  battery  reversed;  7  is 
then  — .  Throughout,  care  must  be  taken  as  to  the  algebraic 
signs  of  all  the  deflections. 

The  final  result  is  independent  of  the  stray  current  in  the  pipe, 
Is',  it$  elimination  is  possible,  even  though  it  be  varying  rapidly, 
because  all  three  instruments  are  read  simultaneously.  The 
periods  and  the  damping  of  the  three  instruments  must  be  such 
that  they  keep  pace*  with  one  another  when  the  current  changes. 

It  will  be  noted  that  if  the  current  7  is  so  adjusted  that  the 
reading  of  V'i  becomes  zero, 

I    =    Is 


THE  MEASUREMENT  OF  CURRENT  97 

and  the  reading  of  the  ammeter  gives  the  strength  of  the  stray 
current.  This  method  of  measuring  the  current  requires  that 
the  observer  remain  continuously  at  his  station.  It  is  frequently 
desirable  to  obtain  records  extending  over  a  considerable  time, 
in  which  case  the  resistance  of  a  section  of  pipe  may  be  determined 
as  above  and  a  registering  millivoltmeter  used. 

References 

1.  "'The  Work  of  Lord  Kelvin  in  Telegraphy  and  Navigation,"  J.  A. 
EWING,  Journal  Institution  of  Electrical  Engineers,  vol.  44,  1910,  p.  538. 

2.  "On  the  Magnetic  Shielding.  Effects  of  Tri-lamellar  Spherical  and  Cylin- 
drical   Shells,"  A.  P.  WILLS,  Physical  Review,  vol.  9,  1899,  p.  193.     "On 
Magnetic  Shielding,"  A.  P.  WILLS,  Physical  Review,  vol.  24,  1907,  p.  243. 

3.  "On  the  Production,  Properties  and  Some  Suggested  Uses  of  the  Finest 
Threads,"  C.  VERNON  BOYS,  Phil.  Mag.,  vol.  23, 1887,  p.  489.     "On  the  Elas- 
tic Constants  of  Quartz  Threads,"  RICHARD  THRELFALL,  Phil.  Mag.,  vol. 
30,  1890,  p.  99.     "The  Attachment  of  Quartz  Fibers,"  C.  VERNON  BOYS, 
Phil  Mag.,  vol.  37,  1894,  p.  463.     "Quartz  Fibers,"  C.  VERNON  BOYS,  The 
Electrician,  vol.  38,  1896-97,  p.  205. 

4.  "  Galvanometers,"  W.E.  AYRTON,T.  MATHER,  and  W.  E.  SUMPNER,  Phil. 
Mag.,  vol.  30, 1890,  p.  58;  Phil.  Mag.,  vol.  46, 1898,  p.  359.     "Instruments and 
Methods  of  Radiometry,"W.W.  COBLENTZ,  Bulletin,  Bureau  of  Standards, vol. 
4, 1907,  p.  424.     "The  Construction  of  a  Sensitive  Galvanometer  for  Spectro- 
Bolometric    Purposes,"    C.  G.  ABBOT,  The  Astrophysical  Journal,  vol.  18, 
July,  1903,  p.  1.     See  also  Annals  of  the  Astrophysical  Observatory  of  the 
Smithsonian  Institution,  vol.  1,  1900,  p.  244,  section  on  Galvanometers. 

5.  "A  Convenient  Form  of  Galvanometer  with  Magnetic  Shielding," 
E.  F.  NICHOLS  and  S.  R.  WILLIAMS,  Physical  Review,  vol.  27,  1908,  p.  250. 

6.  " Galvanometre  Absolument  Astatique  et  a  Grande  Sensibilite,"  M.  A. 
BROCA,  Journal  de  Physique,  vol.  6,  3rd  series,  1897,  p.  67. 

7.  "Some  Properties  of  the   Moving-coil   Galvanometer,"   WALTER  P. 
WHITE,  Physical  Review,  vol.  22,  1906,  p.  371.     "Everyday  Problems  of  the 
Moving-coil  Galvanometer,"  WALTER  P.  WHITE,  Physical  Review,  vol.  23, 
1906,  p.  382.     "Sensitive  Moving-coil  Galvanometers,"  WALTER  P.  WHITE, 
Physical  Review,  vol.  19,  1904,  p.  304.     "Das  Drehspuelengalvanometer  nach 
Deprez-d'Arsonval    im    aperiodischen    Grenzfall,"   W.   JAEGER,   Zeit.  fur 
Instrumentenkunde,  vol.  23,  1903,  p.  261.     Die  Empfindlichkeit  des  Dreh- 
spuelengalvanometers  im  aperiodischen   Grenzfall,"   W.  JAEGER,  Zeit.  fur 
Instrumentenkunde,   vol.    23,  1903,    p.   353.    "General  Design  of  Critically 
Damped   Galvanometers,"  FRANK  WENNER.     Bureau  of  Standards  Scien- 
tific Paper  No.    273. 

8.  "On  the  Use  of  Chilled  Cast  Iron  for  Permanent  Magnets,"  A.  CAMP- 
BELL, Phil.  Mag.,  vol.  12,  1906,  p.  468.     "On  theTemperature  Coefficient  of 
Magnets  Made  of  Chilled  Cast  Iron,"  B.  O.  PEIRCE,  Proc.  American  Academy 
of  Arts  and  Sciences,  vol.  38,  1902-03,  p.  551. 

7 


98  ELECTRICAL  MEASUREMENTS 

9.  "Ein  neues  Galvanometer,"  W.  EINTHOVEN,  Annalen  der  Physik,  4th 
series,  vol.  12,   1903,  p.    1059.     "Theory  of  the  String   Galvanometer  of 
Einthoven",  ALBERT  C.  CEEHORE,  Phil.  Mag.,  vol.  28,  1914,  p.  207. 

10.  "tTber  eine  neue  Method  fur  Dampfung  Oszilierender  Galvanometer 
Auschlag,"  W.  EINTHOVEN,  Annalen  der  Physik,  vol.  16,  1905,  p.  20. 

11.  "tlber     eine     Vorrichtung      um      Messinstrumente      gegen     des 
erschiitteruhgen  des  Bodens  zu  schiitzen,"  W.  H.  JULIUS,  Wied  Annalen, 
1895,  vol.  56,  p.  151. 

12.  "A  Universal  Shunt  Box  for  Galvanometers,"  W.  E.  AYRTON  and  T. 
MATHER,  The  Electrician,  vol.  32,  1893-94,  p.  627. 

13.  "High   Frequency  Ammeters,"   J.   H.   BELLINGER,   Bulletin   of   the 
Bureau  of  Standards,  vol.  10,  1914,  p.  91. 

14.  "Absolute  Measurements  in  Electricity  and  Magnetism,"  A.  GRAY, 
vol.  2,  part  I,  p.  275.     "The  Gray  Absolute  Electrodynamometer,"  E.  B. 
ROSA,  Bulletin  of  the  Bureau  of  Standards,  vol.  2,  1906,  p.  71. 

15.  "A    Tubular    Electrodynamometer    for    Heavy    Currents,"    P.    G. 
AGNEW,  Bulletin  of  the  Bureau  of  Standards,  vol.  8,  1912,  p.  651. 

16.  "A  Determination  of  the  International  Ampere  in  Absolute  Measure," 
E.  B.  ROSA,  N.  E.  DORSEY  and  J.  M.  MILLER,  Bulletin  of  the  Bureau  of 
Standards,  vol.  8,  1912,  p.  269.     "A  New  Current  Weigher  and  a  Deter- 
mination   of  the  Electromotive  Force    of    the    Normal  Cadmium    Cell," 
W.  E.  AYRTON,  T.  MATHER  and  F.  A.  SMITH,  Phil.  Trans,  of  the  Royal 
Society,  vol.  207,  Collected  Researches,  Nat.  Phys.  Lab.,  vol.  4,  1908,  p.  3. 

17.  "Measuring  Stray  Currents  in  Underground  Pipes,"  CARL  HERING, 
Trans.  A.  I.  E.  E.,  vol.  31,  1912,  p.  1449. 


CHAPTER  II 
THE  BALLISTIC  GALVANOMETER 

In  the  comparison  of  the  electrostatic  capacities  of  condensers 
and  cables,  and  in  the  examination  of  the  magnetic  properties  of 
iron,  an  instrument  is  necessary  which  will  measure  the  quantity 
of  electricity  displaced  in  a  circuit  by  a  transient  current.  For 
this  purpose  the  ballistic  galvanometer  is  employed,  and  to  avoid 
disturbances  due  to  local  magnetic  fields  an  instrument  of  the 
D'Arsonval  type  is  now  generally  used. 

For  reading  the  instrument,  a  telescope  and  a  uniformly 
divided  circular  scale,  having  its  center  at  the  axis  of  the  movable 
system,  should  be  employed ;  with  this  arrangement  the  deflection 
as  read  from  the  scale  is  directly  proportional  to  the  angle  turned 
through  by  the  movable  system. 

Observations  are  made  as  follows:  The  movable  system  is 
brought  to  rest  in  its  proper  zero  position;  the  discharge  is  then 
passed  through  the  instrument,  giving  an  impulse  to  the  movable 
system,,  which  slowly  deflects;  the  reading  is  taken  at  the  first 
turning  point,  or  elongation,  just  as  the  movable  system  is  about 
to  begin  its  swing  back  towards  zero.  If  this  maximum  angular 
deflection  of  the  coil  from  its  original  position  be  called  0i  and 
Q  be  the  quantity  of  electricity  in  the  discharge,  then  when  a 
D'Arsonval  instrument  is  employed, 

Q  =  K'Bi 

For  any  particular  instrument  used  in  a  definite  manner  K'  is  a 
constant.  As  will  be  shown  later,  its  value  depends  on  the  cur- 
rent sensitivity  of  the  instrument,  on  the  time  of  vibration  of  the 
movable  system,  on  the  amount  of  damping  and  on  the  manner 
in  which  the  discharge  is  sent  through  the  galvanometer. 

The  ballistic  instrument  differs  from  the  ordinary  current 
galvanometer  in  one  essential  particular,  in  that  the  moment  of 
inertia  of  the  movable  system  is  made  very  large  compared  with 

99 


100 


ELECTRICAL  MEASUREMENTS 


the  restoring  moment  due  to  the  suspension  strip.  In  other 
words,  the  instrument  is  one  having  a  long  time  of  vibration. 
This  is  necessary  in  order  that  the  response  to  the  impulse  caused 


FIG.  51. — Long-period  ballistic  galvanometer. 

by  the  passage  of  the  transient  current  may  be  rendered  so  slug- 
gish that  the  entire  quantity  due  to  the  discharge  of  the  condenser 
or  the  change  of  magnetic  flux  may  have  time  to  pass  through  the 
instrument  before  the  system  has  deflected  appreciably.  In  the 


THE  BALLISTIC  GALVANOMETER 


101 


ordinary  discussion  of  the  ballistic  galvanometer  this  is  assumed 
to  be  true,  but  in  certain  cases  the  assumption  is  not  tenable. 

Some  of  the  devices  for  obtaining  a  large  moment  of  inertia 
are  indicated  in  Fig.  52. 

No.  1  is  for  the  Kelvin  galvanometer,  while  the  others  are  for 
the  D'Arsonval  type.  In  1  and  2  the  crossbar  is  of  aluminum 
with  a  screw-thread  on  it ;  the  little  non-magnetic  weights  are  thus 
made  adjustable.  In  3  the  weights  may  be  removed  from  the 
pans  and  others  substituted  as  desired.  Instruments  of  very 
long  period  may  have  the  moment  of  inertia  increased  as  shown  in 
Fig.  51.  The  rim  of  the  disc,  seen  just  below  the  movable  coil, 
is  made  of  brass,  the  web  of  aluminum. 


FIG.  52. — Suspended  systems  for  ballistic  galvanometer. 

The  time  of  vibration  which  it  is  necessary  to  give  the  movable 
system  in  order  to  obtain  accurate  results  depends  entirely  on 
the  use  to  which  the  instrument  is  to  be  put.  In  comparing 
condensers,  when  the  resistance  of  the  circuit  is  low,  the  discharge 
is  practically  instantaneous  and  an  instrument  with,  a  period 
of  about  20  sec.  is  convenient;  so  long  a  period  is  not  necessary 
in  this  case  for  the  fulfilment  of  the  assumption  that  the  en- 
tire discharge  has  passed  before  the  movable  system  has  been  de- 
flected appreciably,  but  it  renders  the  reading  of  the  instrument 
much  easier.  For  magnetic  work  with  the  usual  small-sized 
specimens  such  a  period  would  be  adequate,  but  for  investiga- 
tion of  the  behavior  of  massive  electromagnets,  an  instrument 
with  so  short  a  period  would  be  of  no  value  whatsoever,  since 
in  this  case  the  change  of  flux  is  very  slow.  When  a  solid  iron 
core  is  tested  as  much  as  30  sec.  may  elapse  before  the  change 
in  flux  is  practically  complete ;  for  suph  work  a  galvanometer  with 
a  period  as  great  as  600  sec.  is  sometimes  employed. 

If  the  motion  of  the  movable  system  results  from  a  series  of 


102 


ELECTRICAL  MEASUREMENTS 


impulses  given  as  the  coil  swings  from  its  zero  position,  or  if  it 
be  due  to  a  prolonged  discharge,  the  magnitude  of  the  deflection 
will  be  affected  by  an  amount  which  will  depend  on  the  manner 
in  which  the  galvanometer  current  varies. 

It  is  frequently  stated  that  one  of  the  essential  characteristics 
of  a  ballistic  galvanometer  is  absence  of  damping,  or,  as  damping 
must  of  necessity  be  present  to  a  certain  degree,  that  it  must  be 
reduced  to  a  minimum.  This  does  not  mean,  however,  that  a 
dampe  mnstrument  cannot  be  used  ballistically;  in  fact,  a  critic- 
ally dadiped  ballistic  galvanometer  is  frequently  most  convenient, 
it  being  a  great  timesaver.  The  damping  should  be  electro- 
magnetic; the  law  governing  it  is  then  definite  and  capable  of  a 
simple  mathematical  expression.  If  air  damping  be  present,  the 
proviso  that  it  be  small  is  a  safe  one,  for  its  law  is  not  exactly 

known.  In  the  analytical 
theory  it  is  assumed  to.be  the 
same  as  for  electro-magnetic 
damping. 

Checking  Devices. — If 
there  be  little  damping,  it  is 
necessary  in  order  to  econo- 
mize time  to  have  some  form 
of  checking  device  by  which 
the  moving  system  may  be 
For  general  purposes,  that  shown  in 


FIG.  53. — Checking  device  for  ballistic 
galvanometer. 


brought  promptly  to  rest. 
Fig.  53  is.  convenient. 

By  a  little  practice  the  motion  of  the  magnet  and  the  manipula- 
tion of  the  key  may  be  so  timed  that  the  zero  is  promptly  attained. 
A  key  in  series  with  a  resistance  placed  across  the  galvanometer 
terminals  is  frequently  convenient;  the  resistance  should  be  of 
such  a  value  that  the  instrument  may  be  critically  damped. 
Thermo-electric  currents  are  frequently  present  and  somewhat 
complicate  the  action  of  these  devices. 

Precautions  in  Reading1. — Trouble  is  likely  to  be  experi- 
enced with  galvanometers  of  the  D'Arsonval  form,  due  to 
changes  in  direction  of  the  very  weak  magnetism  of  the  sup- 
posedly non-magnetic  coil,  and  also  possibly  to  "set"  in  the  sus- 
pension. Both  of  these  must  be  reduced  to  a  minimum  in  the 
manufacture  of  the  instrument,  the  first  by  the  use  of  a  radial 


THE  BALLISTIC  GALVANOMETER  103 

field  and  extreme  care  in  the  preparation  of  the  materials  used, 
and  in  the  winding  of  the  coil.  The  "set"  may  be  minimized  by 
the  proper  choice  of  suspension  strip  and  by  care  in  mounting  it. 

When  readings  are  made  they  should  all  be  taken  toward  the 
same  end  of  the  scale  and  the  coil  should  not  be  allowed  to  swing 
very  much  beyond  zero  on  its  return;  proper  damping  or  use  of 
the  checking  device  will  insure  this.  Before  taking  any  readings, 
a  deflection  in  the  proper  direction  and  as  large  as  any  which  are 
to  be  used  should  be  given  the  system ;  after  this  there  will  be  no 
appreciable  change  of  zero.  This  precaution  should  be  taken 
each  time  the  instrument  is  used. 

If  it  is  necessary  to  take  a  reading  when  the  coil  is  not  abso- 
lutely at  rest,  but  swinging  so  that  the  amplitude  as  read  on  the 
scale  is  only  a  small  fraction  of  a  centimeter,  the  impulse  shoud 
be  given  to  the  system  when  the  swing  is  at  its  maximum 
and  the  elongation  6  should  be  calculated  from  the  true  mechan- 
ical zero,  not  from  the  scale  reading  when  the  discharge  was 
passed.  This  applies  when  the  swinging  on  either  side  of  the 
mechanical  zero  is  not  more  than  about  3  per  cent,  of  the  first 
elongation,  B\. 

Thermo-electromotive  forces  in  any  part  of  the  circuit  are 
troublesome;  those  arising  in  the  galvanometer  itself  should  be 
minimized  by  shielding  from  draughts  or  anything  which  could 
cause  irregularities  of  temperature.  In  the  best  instruments  the 
binding  posts,  connections  to  the  movable  coil  and  the  coil  itself 
are  all  of  copper.  In  specially  designed  instruments  the  current 
is  not  taken  in  through  the  suspension,  which  may  be  of  steel, 
but  through  spiral  connections  made  of  very  thin  copper  strip. 
This  strip  may  be  made  by  rolling  out  a  fine  wire,  about  No.  40. 
The  spirals  may  be  made  so  delicate  that  they  contribute  prac- 
tically nothing  to  the  restoring  moment. 

The  Calibration  of  a  Ballistic  Galvanometer. — It  will  be  shown 
that  the  quantity  of  electricity  which  is  instantaneously  dis- 
charged through  a  ballistic  galvanometer  is  given  by 

'•«-'© 

where 

T  =  time  of  a  complete  swing. 


104  ELECTRICAL  MEASUREMENTS 

0  =  steady  deflection  caused  by  a  steady  current  of  strength 

Io. 

81  =  first  elongation,  or  throw. 
X  =  logarithmic  decrement,  or  natural  logarithm  of  the 

ratio  of  two  successive  elongations. 

In  the  following  discussion,  if  the  displacement  of  electricity  is 
"instantaneous,"  the  corresponding  value  of  0i  will  be  primed;  if 
the  displacement  is  not  instantaneous  the  prime  will  be  omitted. 

With  any  definite  arrangement  of  the  apparatus 

Q  =  K'Oi'. 

A  determination  of  the  time  of  vibration  and  current  sensitivity, 
together  with  X,  enables  the  constant  of  the  instrument  to  be 
calculated.  For  most  purposes,  however,  it  is  preferable  to 
calibrate  by  discharging  a  known  quantity  of  electricity  through 
the  galvanometer  and  reading  the  corresponding  deflection  61 '. 
If  X  at  calibration  differs  from  its  value  during  the  subsequent 
work,  it  must  be  determined  and  allowed  for. 

To  obtain  a  definite  quantity  of  electricity  an  earth  inductor, 
a  mutual  inductance,  or  a  standard  condenser  charged  to  a  known 
voltage  may  be  employed. 

The  earth  inductor  is  a  large  coil  of  many  turns  mounted  on  a 
vertical  or  horizontal  axis  so  that  it  can  be  quickly  turned  through 
90°  or  180°.  The  total  area  of  the  turns  is  known.  The  coil  is 
included  in  the  galvanometer  circuit.  If  the  plane  of  the  coil  is 
originally  in  the  magnetic  meridian  and  the  rotation  is  through 
90°  about  a  vertical  axis,  the  quantity  of  electricity  displaced  in 

the  circuit  is  Q  =  -  —  A  is  the  total  area  of  the  turns,  H  the  hori- 
zontal intensity  of  the  local  field  and  r  the  resistance  of  the  galva- 
nometer circuit.  Owing  to  erratic  variations  of  the  local  field,  this 
method  of  calibration  has  ceased  to  be  of  importance. 

Duddell  has  developed  the  idea  embodied  in  the  earth  inductor 
so  that  an  instrument  of  practical  value  has  resulted.  In  his 
magnetic  standard  two  movable  coils  arranged  astatically  are 
used  in  series  with  the  galvanometer  and  the  local  field  is  replaced 
by  the  fields  due  to  two  oppositely  wound  fixed  coils,  one  acting 
on  each  movable  coil.  On  releasing  a  catch  the  movable  system 


THE  BALLISTIC  GALVANOMETER 


105 


is  rotated  through  180°  by  a  spring,  thus  cutting  the  lines  due  to 
the  fixed  coils. 

This  is  a  secondary  instrument.     The  number  of  lines  cut 
by  the  movable  coils  is 

n  =  KI 

where  /  is  the  current  in  the  fixed  coils  and  K  an  experimentally 
determined  constant  the  value  of  which  is  furnished  by  the  instru- 
ment maker.  It  is  seen  that  the  number  of  lines  cut  may  be 
varied  by  altering  the  current  through  the  fixed  coils. 


FIG.  53a. — Duddell  inductor. 

When  a  mutual  inductance  is  employed,  the  galvanometer  is 
placed  in  series  with  the  secondary  winding.  The  primary  cir- 
cuit may  be  arranged  so  that  a  measured  value  of  the  current 
may  be  suddenly  reversed.  In  this  case 


Q 


2ml 


(1) 


where  m  is  the  mutual  inductance,  /  the  primary  current  and  r 
the  resistance  of  the  secondary  or  galvanometer  circuit. 

A  common  form  of  mutual  inductance  used  for  this  purpose 
consists  of  a  long,  straight  primary  coil  of  one  layer  wound  on  a 
non-magnetic  core,  and  a  short  secondary  coil  wound  outside  the 


106 


ELECTRICAL  MEASUREMENTS 


primary.      The    arrangement,    commonly    called    a    solenoidal 
inductor,  is  indicated  in  Fig.  54. 


Exploring 
Coil 


Am. 


Sec. 

FIG.  54. — Solenoidal  inductor. 

Let  I  be  the  length  of  the  primary  coil,  a  its  radius,  nP  the 
number  of  primary  turns  per  unit  length,  Ns  the  total  number 
of  secondary  turns  and  A  the  cross-section  of  the  primary.  Then 
if  I  is  many  times  a  the  mutual  inductance  is  approximately 


and 


m  =  4:TrnPNsA 


n 

Q  = 


all  quantities  being  in  the  c.g.s.  system, 


or 


(2) 


Q,  I  and  r  in  the  practical  system. 

Ordinarily  when  this  method  of  calibration  is  employed,  the 
instrument  is  to  be  used  in  a  closed  circuit.  The  damping  will 
therefore  be  dependent  on  r  and  the  constant  of  the  galvanometer 
becomes  a  function  of  the  resistance  of  the  circuit.  For  this 
reason,  it  is  common  in  magnetic  work  to  arrange  the  apparatus 
so  that  the  secondary  of  the  calibrating  solenoid  is  continuously 
kept  in  circuit  with  the  galvanometer  and  the  exploring  coil.  A 
substitution  method  is  customarily  used.  First,  a  known  change 
of  flux  is  produced  in  the  circuit  by  the  mutual  inductance  and 
the  change  of  flux  per  scale  division  of  the  galvanometer  thus 
determined.  After  this,  an  observation  of  0/,  corresponding  to 
any  change  of  flux  in  the  specimen,  enables  the  change  in  linkages 
to  be  calculated.  If  r  is  altered,  recalibration  is  necessary. 


THE  BALLISTIC  GALVANOMETER  107 

Concerning  the  use  of  standard  condensers,  see  page  357. 

Theory  of  the  Undamped  Ballistic  Galvanometer.  —  A  D'Arson- 
val  galvanometer  with  a  uniform  radial  field  will  be  assumed. 
With  such  an  instrument  when  it  is  traversed  by  a  steady  current 
of  strength  7G, 

IGC    =    Td 

C  is  the  coil  constant  or  factor  which  when  multiplied  by  the 
galvanometer  current  gives  the  turning  moment  acting  on  the 
movable  system.  Its  value  depends  on  the  strength  of  field,  the 
length  of  active  wire  and  the  breadth  of  the  coil,  r  is  the  torsion 
constant  of  the  suspension,  or  the  restoring  moment  per  unit 
angular  deflection;  rQ  is  then  the  restoring  moment  due  to  twisting 
the  strip  through  an  angle  6. 

It  will  be  necessary  to  recall  that  when  a  body  having  a  moment 
of  inertia,  P,  is  rotating  about  a  fixed  axis  with  an  angular  veloc- 


ity, -77,  its  kinetic  energy  is  given  by  E  =  /^jj     5  that  when 

a  body  so  rotating  has  its  angular  velocity  changed,  the  moment 

d^f)  *     cl^O 

of"  the  forces  producing  the  change  is  M  =  Pj^r,  where  -^  is 

the  angular  acceleration. 

Suppose  the  coil  to  be  at  rest  in  its  zero  position  and  a  tran- 
sient current  whose  intensity  at  any  instant  is  iG  to  be  sent 
through  the  instrument.  Its  electromagnetic  action  gives  rise 
to  a  force  which  lasts  for  the  very  short  time  during  which  the 
current  flows.  This  imparts  a  certain  amount  of  energy  to  the 
movable  system,  which  swings  to  its  extreme  deflection  in  oppo- 
sition to  the  restoring  force  due  to  the  suspension.  At  any 
instant  the  total  energy  of  the  system  is  in  part  kinetic  and  in 
part  the  potential  energy  stored  in  the  twisted  suspension.  When 
the  coil  swings  through  its  zero  position  all  the  energy  is  kinetic, 
while  at  the  end  of  the  swing  it  is  all  potential.  These  two 
amounts  of  energy  must  be  equal,  for  by  supposition  there  is  no 
damping  and  therefore  no  dissipation  of  energy  as  the  coil  swings. 

The  turning  moment  acting  on  the  coil  at  any  instant  is 

iGC  -  r6 


108  ELECTRICAL  MEASUREMENTS 

It  is  assumed  that  the  time  occupied  by  the  passage  of  the 
current  is  so  short  that  the  coil  has  not  moved  appreciably  from 
its  zero  position;  in  other  words,  during  the  discharge  rd  is  zero. 

/(* 
iodt  =  P  I  -jT^dt. 
t/   tl£ 

Therefore,  if  Q  is  the  total  quantity  in  the  discharge, 


0=0 
\di)         *s  ^e  angular  velocity  at  the  zero  position  of  the 

movable  system,  that  is,  at  the  time  when  all  the  energy  is 
kinetic.     The  energy  imparted  to  the  system  is  then 


•  -  «*   . 


2  ^2/12 


The  coil  deflects  and  this  amount  of  energy  is  expended  in  twist- 
ing the  suspension  through  an  angle  0/.  The  coil  then  swings 
back  through  its  zero  position  and  continues  to  oscillate. 

The  work  done  in  twisting  the  suspension  through  the  angle  0/ 
is 

W  = 

As  by  supposition  there  is  no  dissipation  of  energy  during  the 
swing  from  0  =  0  to  0  =  0/, 


8 1  is  the  first  throw  or  elongation.  The  quantities  P,  r  and  C  are 
not  easily  determined  and  the  formula  may  be  put  in  a  more 
useful  shape  by  introducing  the  time  of  vibration  of  the  movable 
system  considered  as  a  torsion  pendulum.  If  T0  be  the  time  of 
vibration  when  there  is  no  damping, 

To  =  2 


THE  BALLISTIC  GALVANOMETER  109 

Hence 


-(£)(>• 


There  still  remains  the  factor  ^-     This  may  be  evaluated  as 

follows:  If  a  current  of  constant  intensity,  IG,  be  sent  through 
the  instrument,  a  deflection  of  constant  magnitude  6  will  result 
and 

C1  ~'    0 


Obviously,  the  ratio  of  the  ballistic  to  the  current  sensitivity  is 

2rr 
To' 

Formula  for  the  Kelvin  Galvanometer. — With  a  Kelvin  instru- 
ment the  work  done  in  turning  the  suspended  system  through  an 

f)f 

angle  0'i,is  MH(l  —  cos  0'i)  =  2MH  sin  2  2  ,  where  M  is  the  mag- 
netic moment  of  the  movable  system  and  H  the  strength  of  the 
controlling  field. 

The  moment  of  the  force  due  to  the  current  in  the  coils  is  at 
any  instant  GiM  cos  6,  where  G  is  the  galvanometer  constant  or 
strength  of  field  at  the  needle,  due  to  a  unit  current  in  the  coils. 
The  time  of  vibration  of  the  needle  system  considered  as  a  mag- 
netic pendulum  is 


Therefore,  in  this  case,  the  expression  for  Q  is 

rr   TJ  a' 


Theory  of  the  Damped  Ballistic  Galvanometer. — In  the  practi- 
cal case  a  certain  amount  of  damping  is  always  present.  It  may 
be  due  to: 

1.  Induced  currents  set  up  in  the  metallic  parts  of  the  movable 
system  by  their  motion  through  the  field  of  the  instrument. 


110  ELECTRICAL  MEASUREMENTS 

2.  Modification   of  the   current  through  the  instrument  by 
the  electromotive  force  induced  in  the  movable  coil  by  its  motion. 

3.  Air  friction. 

4.  Internal  friction  in  the  suspension  wire. 

In  the  D'Arsonval  type  of  instrument,  4  is  entirely  negligible 
and  3  is  small. 

As  the  ballistic  galvanometer  is  ordinarily  used,  the  time  during 
which  the  current  flows  is  very  short.  But  cases  arise  where  the 
displacement  of  electricity  through  the  instrument  is  not  instan- 
taneous, and  such  cases  must  be  included  in  the  general  discus- 
sion.3 

The  ballistic  galvanometer  is  commonly  employed  : 

(a)  In  the  determination  of  magnetic  fluxes. 

(6)   In  the  comparison  of  capacities. 

In  case  (a)  the  instrument  is  used  in  a  closed  circuit,  consisting 
of  the  galvanometer  and  of  the  exploring  coil  wound  around  the 
specimen. 

In  any  case  where  the  instrument  is  used  in  a  closed  circuit 
of  resistance,  r,  the  equation  governing  the  motion  is  (see  page  40) 


k'  is  the  damping  coefficient  when  the  instrument  is  on  open  cir- 

C2 
cuit  and  -  —  is  the  damping  coefficient  due  to  the  e.m.f.  set  up  in 

T  • 

the  main  circuit  by  the  motion  of  the  coil.     In  this  discussion 
let 


e  is  the  instantaneous  value  of  the  e.m.f.  impressed  on  the  circuit; 
it  is  a  function  of  t,  and  usually  becomes  zero  in  a  comparatively 

short  time.  —  L  -j.  is  the  back  e.m.f.  due  to  the  inductance  of 
dt 

the  galvanometer  circuit.     In  the  following  discussion  it  will  be 
assumed  to  be  negligible. 

If  the  conditions  are  such  that  the  current  through  the  instru- 
ment is  not  modified  by  the  e.m.f.  due  to  the  motion  of  the 

C2 
coil,  then  in  (4)  the  term  —  is  absent  and  the  second  member 


r 


THE  BALLISTIC  GALVANOMETER  .111 

becomes  Ci.     The  process  of  solution  for  I  idt    is    the   same   as 

Jo 

f*t 

that  employed  below  for 


•  I  edt. 
Jo 


di 
Assuming  that  L       is  negligible,  the  solution  of  (4)  is* 


"'  +  C2e-2< 

c 


r    emi<  I  ee~mi'  dt  —  €m2«  I  ee-m2<  ^ 

-  w2)  L    J  j 


rP  (mi      —-M  *  ~  I  ""     "  **•       *  -   §  ^     -  ">*  i      (5) 

The  values  of  mi  and  w2  are  given  on  page  26. 

When  the  e.m.f.  is  first  applied  to  the  circuit  the  movable  system 

is  supposed  to  be  at  rest  in  its  zero  position;  that  is,  when 

t  =  0,         0=0.     and    ^-  =  0 
Since  e  is  a  function  of  t  these  conditions  are  imposed  if 

(6) 


rP(mi- 
and 


T^k  /  \ 

rP(mi  -  w2) 


[/< 


(7) 


With  these  values  of  Ci  and  C2  substituted  in  (5)  the  deflection  at 
any  definite  time,  t,  is 


7          T       f  f  1 

—V   emi<  I   ee-ni'dt  —  e™*'  I   ee'^dt 
-  W2)  L       Jo  Jo 


Equations  (5)  and  (8)  apply  in  all  cases.  A  difficulty  is  en- 
countered in  using  them,  since  in  comparatively  few  instances 
is  it  possible  to  express  e  as  an  algebraic  function  of  t.  This 
precludes  the  taking  of  the  integrals  by  purely  analytical  methods. 

In  the  preliminary  study  of  a  proposed  investigation,  if  it  is 
found  that  the  displacement  of  electricity  through  the  ballistic 
galvanometer  will  not  be  "instantaneous,"  it  is  necessary  to 
inquire  how  much  the  first  elongation  will  be  influenced  by  the 
manner  in  which  e  varies.  For,  see  pages  105  and  106,  the  galva- 

*  COHEN  "Differential  equations,"  p.  103. 


112  ELECTRICAL  MEASUREMENTS 

nometer  is  calibrated  by  methods  in  which  e  is  applied  to  the 
circuit  "instantaneously." 

To  obtain  the  necessary  data,-  the  logarithmic  decrement  and 
the  time  of  vibration  must  be  found  and  a  preliminary  test  made 
which  will  experimentally  determine  the  curve  connecting  e  and 
t.  This  curve  must  be  one  that  fairly  represents  the  conditions 
which  will  exist  in  the  subsequent  work,  and  is  to  be  used  as 
described  below.  If  the  computations  show  that  the  first  elonga- 
tion will  be  greatly  influenced  by  the  manner  in  which  the  dis- 
charge is  sent  through  the  galvanometer,  it  will  be  necessary  to 
modify  the  instrument  by  giving  it  a  longer  period  of  vibration. 

Suppose  that  the  experimentally  determined  graph  connecting 
e  and  t  shows  that  e  has  become  sensibly  equal  to  zero  before  the 
galvanometer  deflection  has  reached  its  first  elongation.  If  the 
time  which  elapses  before  e  becomes  sensibly  equal  to  zero  be 
denoted  by  t',  the  values  of  the  integrals  in  (8)  taken  for  times 
greater  than  t'  are  practically  constant.  In  the  case  where  the 
galvanometer  is  over-damped,  that  is,  where  mi  and  ra2  are  real,  let 
M  and  N  be  two  quantities  defined  as  follows  : 

/*Sf 

I    ee~m^dt 

M  =        ^==  t,  —  ,  a  constant  (9) 

I    edt 

,    ,  Jo 


i\   =  --  Tn^Tt'  —  >  a  constant  (10) 

edt 


Then 

r  i        c     r  r  *  n  r  i 

\  6  I  =  -  =-; —  6^      Me™!*  —  Nemzt  (11) 

L  J^'  rP(mi  -  ra2)  [Jo        J  L  J^ 

0i,  which  is  the  observed  reading  of  the  instrument,  occurs  at  a 
time  tij  when  -T.   =  0.     Neglecting  the  constant  coefficient  in  (11) 

(Jut 

dO 

-JT  —  Mmit™^  —  Nm^m^  =  0 
at 

or 

/  \Nm2 


THE  BALLISTIC  GALVANOMETER  113 

1  Nmz 

.  .  ti  =  -  -loge  -^ — • 

mi  —  mz         Mmi 

Substituting  this  value  of  ti  in  (11)  gives  for  the  first  elongation 


C 


~  rP(mi  - 


IF] 


mi 


TOI  —  wi2 

\M.m\i 
or 


rP(mi  - 


o 


TO2  

!    —    TO, 


The  quantity  in  the  brackets  { }  depends  only  on  mi  and  w2  and 
is  therefore  independent  of  the  manner  in  which  e  varies.  If  the 
displacement  of  electricity  through  the  galvanometer  is  "  in- 
stantaneous/' that  is,  if  e  goes  through  its  cycle  of  values  "  in- 
stantaneously, "  then  by  (9)  and  (10) 

M  =  1        N  =  1 

Therefore  when  the  motion  of  the  movable  system  is  non-peri- 
odic, the  ratio  of  the  actual  elongation  to  that  which  would 
have  occurred  had  the  same  integral  change  in  e  been  made 
instantaneously  is 

A,  mi  TO2 

l  / 1  o\ 

=      ftfmi    —    mzj(/rm2    —    mi  V-Lt)/ 

O'l 

It  is  seen  that  (13)  gives  a  measure  of  the  error  produced  in  the 
deflection  by  the  prolongation  of  the  discharge  through  the  gal- 
vanometer. 

To  obtain  the  numerical  values  of  M  and  N,  the  ordinates  of 
the  graph  connecting  e  and  t  are  multiplied  by  e~OTl*  and  e"1 
and  the  two  curves  thus  obtained  are  plotted  to  the  original  scale. 
All  three  curves  are  then  integrated  by  a  planimeter  giving  the 
necessary  data  for  calculating  both  M  and  N. 

When  the  motion  of  the  movable  system  is  periodic,  that  is, 

A;2      r 
when  /,TM<D,  mi  and  mz  are  complex. 


114  ELECTRICAL  MEASUREMENTS 

mi  =  —  a  +  jb,     m2  =  —  a  —  jb 


where 


k        2X  27r 

a  =  2P  =''  ^T  =  ~T 


These  values  of  mi  and  m2  when  substituted  in  (8)  give 

c  e~c   ihi  r  fa-flu.    -  ft*  r  <*+#>*  A]  /i/i\ 

0  =     D  •  cJfet     I  ee  at  —  e  \  ee  dt\      (14) 

rP       2ib  Jo  Jo 


but 

ejbt   =   cog  ^i  _j_ 

and 

e-jw  _  eos  5£  _ 

Hence 


Cf-at  ri  ri 

8  =  -pr-[(sin  bt)  I  eeatco$  btdt  -  (cos  60      eeat  sin  btdt]          (15) 
Jo  Jo 

The  method  of  dealing  with  this  equation  when  e  falls  sensibly 
to  zero  before  the  first  elongation  is  reached  is  similar  to 
that  just  employed  in  the  nonperiodic  case.  See  page  112. 

Let  R  and  S  be  defined  as  follows  : 

/*W 

I  eeat  cos  btdt 
R  =         f&t  --  >  a  constant  (16) 

I  edt 

Jo 


eeat  sin  &Zd* 
S  =J*L-  ,  a  constant  (17) 

\edt 
Jo 

Then  when  t  ^  t' 

Ce  ~ at  r  r*  ^  e/i 

0  =  —-—  \  I  edt  I  {R  sin  6«  -  S  cos  bt\  (18) 

^   LJo      J      ^ 

To  find  0i  determine  ti  by  placing  ^r  =  0  and  substitute  the  result 

in  (18).     Neglecting  the  constant  coefficient 

d0 

—  =  e  -  <*{(-  a/^  +  6>S)  sin  bt  +  (a/S  +  bR)  cos  6d  =  0 

.  sin  bti  aS  +  bR       \S  +  TT^ 


ij      —  i    —        7-,  T  CY    —    -v  ?->  rr" 

cos  Wi  a72  —  bS      \R  —  irS 


.":-.: 

THE  BALLISTIC  GALVANOMETER  115 

Substituting  t\  in  (18)  gives 


If  the  same  integral  change  in  e  had  been  made  instantaneously, 
then  by  (16)  and  (17) 

R  =  1        S  =  0 


and  the  deflection  would  have  been 

*'  ^  ''  1         1 

Ljo^Jv^T2  (20) 

It  follows  in  this  case  that 


CT  -xtan-^rr5' 


(2D 


This  quantity  is  a  measure  of  the  error  produced  in  the  de- 
flection by  the  prolongation  of  the  discharge  through  the 
galvanometer. 

The  equations  19  and  20  are  more  conveniently  expressed  if  C 
and  P  are  replaced  by  quantities  which  are  more  easily 
determined. 

Since 

T  =  -  -* 


4X2 

and 

rd  =  IGC, 
substituting  in  (19)  and  solving  for 


IF] 


gives 


IF]  •  ( 


Discussion. — When  the  Displacement  of  Electricity  is  Instan- 
taneous.— The   circuit  in  which  e  acts  contains  the  inductance 


116  ELECTRICAL  MEASUREMENTS 

of  the  galvanometer.  If  e  goes  through  its  cycle  "  instanta- 
neously/' that  is,  in  a  time  so  short  that  the  cycle  is  over  before 
the  coil  of  the  galvanometer  moves  appreciably,  then  as  the 
current  is  zero  both  at  the  start  and  at  the  finish, 


rt  pt^  f 

rl  idt  =  I  edt  =  rQ. 

Jo  Jo 


In   the   case   of   an   instantaneous   displacement   of   electricity 
through  the  instrument  the  quantity,  Q,  is  given  by 


~tan"    r    "'  (23) 


/7T2  +  X2 

This  is  the  formula  commonly  used  for  the  ballistic  galvanometer. 
The  term  involving  X  gives  the  correction  for  damping. 

The  quantity  in  the  brackets    {     }    may  be  expanded  by 
Maclaurin's  theorem,  giving 

1  +  0.5X  -  0.026X2  -  0.055X8   . 


V7T2  +  X2 

and  if  X  is  small, 


For  a  secondary  instrument,  assuming  that  T  is  not  sensibly 
affected  by  any  change  in  damping  which  is  likely  to  be  encoun- 


tered, 

_  „  f          XI 


where  K  is  a  constant. 

Another  approximation  sometimes  used  in  making  the  correc- 
tion for  damping,  results  from  assuming  X  to  be  very  small,  in 
which  case 


7T  t  n-i- 

' 


- 

x  = 


A 

=  e2  approximately. 


T  I 

But,  from  the  law  of  damped  oscillations  (page  30) 
0i 


v  4  "0 

Consequently 

x        /0i\  ^       /0i\ H 

e2  =  y  =  y 


THE  BALLISTIC  GALVANOMETER  117 

and  Q  is  given  approximately  by 


Discussion.  —  TFAen  £/ie  Discharge  through  the  Instrument  is 
Prolonged.  —  If  the  equation  connecting  e  and  t  is  known,  the 
integrations  indicated  in  (5),  (6)  and  (7)  may  be  performed. 
Suppose  for  example  that 


e  = 


In  this  case,  which  is  of  practical  importance4,  the  total  quan- 
tity of  electricity  displaced  in  this  circuit  is 


Q 


=  l-  fedt  =  *• 
rjo  rp 


Substituting  the  value  of  e  in  (5), 

C*~f?       {        *-mit                      -mzt        I  C*~f? 

_C^O_     _€j_ € C£0 

&     —     ~        -n    -1      1  f  I 


2rPjb[p  +  mi       p  +  m2j         rP       (p  +  ra2)(p  +  Wi) 

To  find  <i,  the  time  of  the  first  elongation  or  the  turning  point, 
this  value  of  0  is  differentiated  and  the  result  placed  equal  to 
zero.  Combining  the  equation  so  formed  with  (27)  gives 

1 


0    . 

2rPjbp 


m,t,    ._    ,m* 


or  after  the  values  of  m\  and  ra2  are  substituted, 


. 

Equating    -.,  to  zero  gives  ti,  the  time  of  the  first  elongation,  as 
a  solution  of  the  equation 

2ir 


e  T;      =  cos  I  -^ 


The  value  of  ti  is  obtained  by  successive  approximation. 

Referring  to  (20)  and  (28)  it  will  be  seen  that  the  ratio  of  the 
deflection  to  that  which  would  have  been  obtained  had  the  same 
quantity  been  discharged  through  the  galvanometer  instan- 
taneously is 


118  ELECTRICAL  MEASUREMENTS 


(30) 


This  ratio  gives  a  measure  'of  the  effect  produced  on  the  first 
elongation  by  the  prolongation  of  the  discharge. 

As  another  example,  take  one  which  may  be  realized  by  the 
manipulation  of  the  apparatus  used  for  calibrating  a  ballistic 
galvanometer  by  means  of  a  mutual  inductance. 

Suppose  the  primary  circuit  to  be  traversed  by  a  current.  At 
a  time  t  =  0  the  circuit  is  broken  by  the  reversing  switch. 

77 

This    instantaneously    removes    ~   magnetic  linkages  from  the 

z 

secondary.     After  an  interval  of  10  sec.,  the  circuit  is  made  in 

the   reverse   direction  and  a  second  instantaneous  change  of  ~ 

Z 

linkages  is  made. 

It  is  desired  to  know  how  the  deflection  so  obtained  will  com- 
pare with  that  which  would  have  been  obtained  had  the  change 
of  n  linkages  been  made  instantaneously. 

In  this  case  using  (16)  and  (17) 


R 

t 

f  ^  10 

I  eeat  cos  btdt          -j 

t/  0                                          ^ 

-  ^  e10a  cos  106 

/•«5  10 

J  edt 

Jt^  10 
ee°(  sin  btdt        0  - 

n 
\-  ^  e100  sin  106 

J 


10  n 


edt 
Suppose  the  following  data  apply  to  the  galvanometer  in  question 

Time  of  a  complete  vibration  =  T  =  149  sec. 

n 
Ratio  of  tWo  successive  swings  =  -^  =  1.063. 

Logarithmic  decrement  =  X  =  log€  1.063  =  0.0611. 
6  =  ~  =  0.0422 

0.00082 


THE  BALLISTIC  GALVANOMETER 


119 


Consequently 

R  =  y2[\  +  eo.oo82  cos  0  422]  =  0.9597 
S  =  ^[e0-0082  sin  0.422]  =  0.2064 
V#2  T52  =  0-982 

x      -i  s 
e^tal      R=  eo.oo4i  =  1.004. 

By  (21) 

0i       0.982 


1.004 


=  0.978. 


The  error  is  therefore  2.2  per  cent, 
above  conditions  gave 

-}-  =  0.978. 


An  actual  test  under  the 


When  the  ballistic  galvanometer  is  used  in  series  with  a  test 
coil  for  determining  magnetic  fluxes  through  iron  cores  it  is  not 
possible  to  apply  the  above 
purely  analytical  method,  for 
the  law  connecting  time  and 
the  e.m.f.  induced  in  the  test 
coil  is  not  known.  In  this  case 
the  integration  must  be  made 
with  the  aid  of  a  planimeter. 

The  graph  connecting  e  and 
t  may  be  obtained  by  an  os- 
cillograph, an  exploring  coil 
being  wound  for  that  purpose 
on  the  specimen  under  test. 
In  general,  the  oscillograph  is 
not  inserted  in  the  galvanom- 
eter circuit  for  the 


6      8     10     12     14 
Time,  Seconds 


16     18     20 


FIG.  55. — Pertaining    to    effect    of 
current  prolonged  discharge  through  a  ballistic 
. ,    .  ,.~    ,   ,  e    galvanometer, 

in  it  is  modified  by  the  e.rn.i. 

set  up  by  the  movable  coil.  In  cases  where  this  e.m.f.  is  in- 
significant compared  with  that  due  to  the  change  of  flux  through 
the  circuit,  the  separate  exploring  coil  is  not  necessary.  Suppose 
the  e.m.f.-time  curve  OABC,  shown  in  Fig.  55,  has  been  obtained. 
The  curves  OEC  and  OFC  are  obtained  by  multiplying  the 
ordinates  of  OABC  by  the  corresponding  values  of  e0<  cos  bt 
and  €at  sin  bt. 


120  ELECTRICAL  MEASUREMENTS 

From  the  figure  it  will  be  seen  that  i'  is  20  sec.  This  means 
that  e  is  practically  zero  after  this  time;  in  reality,  a  very  small 
e.m.f.  may  persist  for  a  considerably  longer  period  but  the  quan- 
tity of  electricity  displaced  by  it  may  be  neglected. 


edt   is  obtained    from  the  area  under  the  curve   OABC. 
(o 
Integrating  the  curves  by  a  planimeter,  and  using  (16)  and  (17). 

R  =  0.920 
S  =  0.320 
therefore 

V~R*+~S*  =  0-973 
if  X  =  0.0611 


CT  B    =   60.00li5    =    1.007. 

By  (21) 

f  S2_0973 

~s-   "  1.007  "    °'9b6' 


The  error  due  to  the  prolongation  of  the  discharge  is  3.4  per 
cent,  for  this  particular  form  of  e.m.f.  curve. 

The  Critically  Damped  Ballistic  Galvanometer. — Mathe- 
matically, critical  damping  occurs  when  the  roots  of  the  equation 

k 
Pm2  +  km  +  r  =  0  are  equal,  or  when  mi  =  mz  =  —  op  cor~ 

responding  to 


In  this  case,  the  solution  of  (4)  becomes 

B  =  (d  +  C20e~  ^+  £]  *e~  2p  I  ee^  ^  -  6~  ^  I  /ee^  d<  |          (31) 
rjr  L  »/  «/ 


The  movable  system  is  supposed  to  be  at  rest  in  its  zero  posi- 
tion, when  e  is  applied  to  the  circuit,  that  is,  when 

t  =  0    6  =  0. 

t  =  0  J  =  0. 

d£ 


THE  BALLISTIC  GALVANOMETER  121 

These  conditions  will  be  fulfilled  if 

•  (32) 


so  6  =  ~  €      D  t\eSp  dt  -Ueezpdt  \  (34) 

If  the  integral  change  in  e  is  "instantaneous" 

6  =  -p 
The  first  elongation  occurs  when 

S  =  0  =  1-2?> 

t  .=  2f>  =    IP  =  ^ 

Substituting   this  value  of  £1  gives 


where  0  is  the  deflection  due  to  a  steady  current,  I0. 

It  is  seen  that  the  elongation  is  proportional  to  the  quantity 
of  electricity  in  the  discharge,  and  that  the  galvanometer  factor 
is  e  times  that  of  the  undamped  instrument.  Consequently, 

the  quantity  sensitivity  is  -,  or  37  per  cent  that  of  the  undamped 

instrument.     Also,  the  time  necessary  for  arriving  at  the  elonga- 

2 
tion  0i  is  -,  or  64  per  cent  that  of  the  undamped  instrument. 

7T 

Equation  (36)  applies  when  the  ballistic  galvanometer  is  used 
in  a  series  circuit  ;  the  resistance,  r,  being  such  that  the  galvanom- 
eter is  critically  damped.  When  the  instrumental  constants  used 
in  equation  (4)  are  introduced,  (36)  becomes 


LT-M 


(37) 


122  ELECTRICAL  MEASUREMENTS 

If  the  resistance  of  the  apparatus  to  which  the  galvanometer 
is  attached  is  so  high  that  the  instrument  is  underdamped,  criti- 
cal damping  may  be  obtained  by  shunting  the  galvanometer.  In 
this  case  if  R  is  the  resistance  of  the  apparatus  to  which  the 
galvanometer  is  attached  and  R0  that  of  the  galvanometer, 


[JH-fc 


+  &*'/-  (38) 

As  no  time  is  lost  in  bringing  the  movable  system  to  rest,  the 
critically  damped  ballistic  galvanometer  is  frequently  a  most 
convenient  instrument. 

The  Use  of  Shunts  with  the  Ballistic  Galvanometer. — At  first 
sight  it  would  seem  that  if  a  ballistic  galvanometer  were  shunted 
with  a  non-inductive  resistance,  the  total  quantity  of  electricity 
discharged  from  a  condenser  would  not,  on  account  of  the  in- 
ductance of  the  galvanometer,  divide  inversely  as  the  resistance 
of  the  galvanometer  and  of  the  shunt.  However,  the  quantity 
does  so  divide  as  will  be  seen  from  the  following : 

Let  RO  —  galvanometer  resistance. 
LQ  =  galvanometer  inductance. 
i0  =  galvanometer  current. 

Qo  =  quantity  discharged  through  galvanometer. 
S  =  shunt  resistance. 
Ls  =  shunt  inductance. 
is  =  shunt  current. 

Qs  =  quantity  discharged  through  shunt. 
Then 

,    di0  dis 

**&Q  T  L'o  ~jT   -~  MS  ~t~  J^s  ~Jj ' 

Consequently 

RoQo  ~h  LQJ*di0  =  SQS  +  Lsfdis 

Both  currents  are  zero  at  the  beginning  and  zero  at  the  end 
of  the  discharge,  so 

Qs  =  Ro 

It  is  seen  that  any  error  caused  by  the  shunt  must  be  due  to 
the  variation  of  the  damping  when  the  multiplying  power  is 
changed. 


THE  BALLISTIC  GALVANOMETER  123 

The  total  quantity  of  electricity  discharged  through  a  shunted 
instrument  which  is  slightly  damped  is 

n    (Ro  +  S\        v  1 1    .   XI  (RG  +  S\     , 
Q  =  Qo  ( — g — j   =  K  |1  +  2J  ( — g— J  0  i  nearly  enough. 

Considering  the  damping  to  be  electromagnetic  and  that  the 
shunted  galvanometer  is  used  on  an  open  circuit, 

_  kT  _          C2T 

X         A    ^         


4P       (Rg  +  S)  4P 
* 

6 


.;Q-K 


C2jT 

But  -^^  is  practically  constant.     Therefore  when  the  damping  is 

or 

not  large,  the  multiplying  power  to  be  used  with  ballistic  throws 
may  be  obtained  by  considering  the  galvanometer  resistance  to 
be  increased  by  a  certain  constant  amount  which  depends  upon 
the  construction  of  the  instrument.  The  effective  multiplying 
power  of  the  shunt  is 

(Ra  +  A)  +  S 

m=          -g- 

This  is  Latimer  Clark's  method  of  correction.  The  quantity  A 
may  be  determined  experimentally.  Suppose  a  condenser  to  be 
charged  to  V\  volts  and  discharged  through  the  shunted  instru- 
ment; then 


When   the   condenser  is   charged   to    V2  volts  and   discharged 
through  the  unshunted  galvanometer, 


=  K    0'i2  =  CV2 

+  V  (39) 


A  practical  difficulty  met  with  when  applying  shunts  of  the  ordi- 
nary sort  to  a  moving-coil  ballistic  galvanometer  is  that  the  range 
of  the  instrument  cannot  be  greatly  extended  before  the  damping 
becomes  excessive. 

In  open-circuit  work,  that  is,  in  measurements  upon  condensers 


124 


ELECTRICAL  MEASUREMENTS 


or  cables,  the  universal  shunt  (page  52)  should  be  used.  The 
advantage  of  this  arrangement  is  that  the  resistance  through 
which  the  damping  current,  set  up  by  the  motion  of  the  coil, 
must  flow  is  always  the  same.  Consequently,  X  does  not  vary, 
even  though  the  multiplying  power  of  the  shunt  be  changed. 
Another  advantage  is  that  the  total  shunt  resistance,  r,  may  be 
made  so  great  that  the  instrument  is  not  over-damped,  even 
though  it  is  heavily  shunted. 

Obviously  the  universal  shunt  loses  its  advantages,  if  the  con- 
denser be  replaced  by  a  closed  circuit,  as  an  exploring  coil  for 
magnetic  work. 


FIG.  56.— Flux  meter. 

The  Flux  Meter. — The  flux  meter,6  as  its  name  indicates,  is 
designed  for  measuring  the  flux  in  magnetic  circuits.  This 
instrument  is  essentially  a  moving  coil  ballistic  galvanometer  in 
which  the  restoring  moment  is  reduced  to  a  minimum  by  the 
removal  of  the  controlling  spring.  In  a  perfect  instrument  the 
restoring  couple  would  be  zero;  practically  it  is  difficult  to  reduce 
the  controlling  action  of  the  necessary  leads  to  the  movable  coil 
to  a  negligible  amount  and  usually  after  the  movable  system  has 
been  deflected  it  very  gradually  sinks  back  towards  zero. 

Fig.   56  shows  the  instrument  and   the   suspended  system. 


\ 
THE  BALLISTIC  GALVANOMETER  125 

The  moving  coil  is  hung  by  a  silk  fiber  from  the  spring  support 
R',  the  current  is  led  to  the  coil  through  the  delicate  spirals  S,  S, 
which  are  of  annealed  silver  and  supposed  to  exercise  no  control- 
ling effect  on  the  movable  system.  A  mechanical  device  is  em- 
ployed by  which  the  system  may  be  quickly  reset  to  its  zero 
position. 

The  instrument  is  used  in  series  with  an  exploring  coil  and 
therefore  in  a  closed  circuit.  When  the  change  of  flux  through 
the  test  coil  is  completed,  the  movable  system  comes  to  rest  in  its 
deflected  position  and  the  change  in  linkages  is  given  by 

n  =  C0i  (40) 

which  is  true,  irrespective  of  the  manner  in  which  the  flux  is 
changed  and  of  the  time  occupied  in  making  the  change.  This 
connection  between  the  deflection  and  the  change  of  flux  linkages 
may  be  seen  from  equation  (12). 

When  the  torsional  control,  r,  is  indefinitely  reduced,  mi  and 
/ft  2  which  are  the  roots  of  the  equation  Pm2  +  km  +  T  —  0 
approach  the  values 

mi  =  0 

fc 


Under  these  conditions  (see  page  112). 

M  =  1, 

N  =  some  definite  numerical  value, 


and  the  factor  Nm]  t2  Mm'  ll  in  (12),  which  depends  on  the 
manner  in  which  the  discharge  takes  place,  always  becomes 
unity.  The  factor  in  (12)  which  is  within  the  brackets  also 
approaches  unity,  so  if  n  is  the  total  change  of  flux  linkages 


As 

C2 
fc  =  h  k  i  see  page  110. 


126  ELECTRICAL  MEASUREMENTS 

The  air  damping  is  very  small  so  n  =  C0i,  approximately.     This 
relation  may  be  proved  directly  as  follows. 

Let  n  =  number  of  linkages  of  flux  with  exploring  coil. 
61  =  final  value  of  deflection. 
C  =  coil  constant. 
co  =  angular  velocity  of  movable  coil. 

=  rate  of  change  of  linkages  through  exploring  coil. 


L  =  inductance  of  exploring  coil  circuit. 
P  =  moment  of  inertia  of  movable  system. 
k'  =  damping  constant  for  air  damping. 
r  =  resistance  of  exploring  coil  circuit. 
i  =  current  at  any  instant. 
Nf  =  number  of  turns  in  exploring  coil. 
V  =  flux  through  exploring  coil. 

As  soon  as  the  coil  begins  to  move,  it  sets  up  a  back  e.m.f.  whose 
value  is  co(7. 

The  current  at  any  instant  is 

dn  di 

—  -  Ceo  -L 


and 


dt  -  -  r     dl     '  dt 


At  the  beginning  and  at  the  end  of  the  deflection,  both  co  and 
i  are  zero,  so  on  integrating, 

0  =  —  - 
r 


n  =  (c  +  ~)  0!. 


The  air  damping  is  small.     Very  closely  then  the  change  of  flux 
linkages  is  given  by 

n  =  CBi 
and 


THE  BALLISTIC  GALVANOMETER  127 

hat  is,  the  deflection  is  proportional  to  the  change  in  the  flux 
hreading  the  exploring  coil.  In  the  actual  instrument  the  scale 
is  calibrated  experimentally.  The  advantages  of  the  flux  meter 
over  the  ballistic  galvanometer  are  portability,  ease  of  reading, 
and  independence  of  the  time  required  for  the  flux  changes  and  of 
the  manner  in  which  they  take  place.  It  is  therefore  a  con- 
venient workshop  instrument.  As  ordinarily  constructed,  its 
accuracy  is  inferior  to  that  of  the  ballistic  galvanometer.7 

References 

1.  "On  Precision  Measurements  with  the  Moving  Coil  Ballistic  Galva- 
nometer," ANTHONY  ZELENY,  Physical  Review,  vol.  23,  1906,  p.  399. 

2.  "The  Damped  Ballistic  Galvanometer,"  O.   M.  STEWART,  Physical 
Review,  vol.  16,  1903,  p.  158. 

3.  "The  Theory  of  Ballistic  Galvanometers  of  Long  Period,"  B.  OSQOOD 
PEIRCE,  Proc.  American  Academy  of  Arts  and  Sciences,  vol.  44,  1909,  p.  283. 

4.  "The  Ballistic  Use  of  a  Moving  Coil  Galvanometer  in   Measuring 
Discharges  Obeying  the  Exponential  Decay  Law,"  A.  G.  WORTHING,  Physical 
Review,  vol.  6,  1915,  p.  165. 

5.  "The  Effect  of  the  Time  of  Passage  of  a  Quantity  of  Electricity  on 
the  Throw  of  a  Ballistic  Galvanometer,"  F.  WENNER,  Physical  Review, 
vol.  25,  1907,  p.  139. 

6.  "An    Electric  Quantometer,"  R.  BEATTIE,   The  Electrician,  vol.  50, 
1903,  p.  383.     "Fluxmetre,"  M.  E.  GRASSOT,  Journal    de   Physique,  4th 
series,  vol.  3,  1904,  p.  696. 

7.  "On  the  Determination  of  the  Magnetic  Behaviour  of  the  Finely 
Divided  Core  of  an  Electromagnet  while  a  Steady  Current  is  being  Estab- 
lished in  the  Exciting  Circuit,"  B.  OSGOOD  PEIRCE,  Proc.  American  Academy 
of  Arts  and  Sciences,  vol.  43,  1907,  p.  99. 


Btass  Tube 


CHAPTER  III 
RESISTANCE  DEVICES 

The  resistance  devices  used  in  electrical  measurements  may  be 
divided  into  two  groups,  resistance  boxes  and  rheostats. 

A  resistance  box  is  a  device  by  which  the  resistance  of  a  circuit 
may  be  altered  by  accurately  known  amounts.  It  contains  an 
aggregation  of  coils,  each  coil  having  a  definite  and  known 
resistance,  and  the  construction  is  such  that  the  coils  may  be 
connected  in  various  combinations  so  that  any  required  resistance, 
up  to  the  full  capacity  of  the  box,  may  be 
obtained. 

The  term  rheostat  is  applied  to  the  de- 
vices commonly  used  for  varying  the  re- 
sistance of  the  circuit  where  regulation  of 
currents  and  absorption  of  power  are  con- 
cerned. The  circumstances  under  which 
rheostats  are  used  render  it  unnecessary 
that  the  magnitudes  of  the  variations  in 
resistance  be  known. 

Resistance  Coils. — Formerly  it  was  the 
universal  practice  to  wind  resistance  coils 
on  wooden  bobbins,  but,  in  the  better  class 
of  work,  these  bobbins  have  been  replaced 
by  metal  spools  (see  Fig.  57).  A  layer  of 

shellaced  silk  which  is  dried  out  by  baking  before  the  coil  is 
wound  serves  to  thoroughly  insulate  the  wire  from  the  metal 
spool. 

Non-inductive  windings  are  always  employed.  The  wire  is 
arranged  in  a  bight  before  it  is  wound  upon  the  bobbin  and  the 
two  wires  are  kept  side  by  side  in  the  coil. 

If  possible,  the  winding  is  concentrated  in  a  single  layer,  for 
as  all  the  heat  must  be  dissipated  through  the  surfaces  of  the 
coil,  one  wound  several  layers  deep  with  a  large  wire  is  not  supe- 
rior to  one  wound  with  but  a  single  layer  of  small  wire. 

128 


Binding 
Silk  — 


•^-Resistance 

Wire 

*— -Brazed 
Copper 
"Soldered 

FIG.  57. — Section  of  re- 
sistance coil. 


RESISTANCE  DEVICES  129 

After  it  is  wound,  the  coil  is  shellaced  and  then  baked  for 
10  hours  or  more  at  140°C.;  this  frees  the  entire  coil  of  moisture 
and  alcohol  and  at  the  same  time  anneals  the  wire.  After  baking, 
the  coil  should  be  given  a  protective  coating  of  paraffin. 

The  resistance  wires  are  hard-soldered  to  copper  terminals 
which  in  turn  are  soft-soldered  to  the  working  terminals. 

The  prime  requisite  of  the  resistance  material  used  for  winding 
coils  is  permanence.  In  additidn,  its  temperature  coefficient 
should  be  small,  its  thermal  e.m.f.  when  opposed  to  copper,  low, 
and  to  obtain  compactness,  its  resistivity  should  be  high.  Alloys 
rather  than  the  pure  metals  are  used  for  they  have  smaller  tem- 
perature coefficients  and  higher  resistivities.  To  settle  the  all- 
important  question  of  permanence  prolonged  investigation  is 
of  course  necessary.  Up  to  the  present  time,  the  alloy  which 
has  most  commended  itself  is  that  known  as  manganin.2 
Other  alloys  are  used  for  certain  kinds  of  work  but  manganin 
has  been  under  critical  examination  longer  than  the  others  and 
its  properties  are  more  definitely  known. 

Edward  Weston  discovered  in  1889,  that  alloys  of  copper  and 
nickel  containing  some  manganese  have  very  small  temperature 
coefficients  and  high  resistivities.  Investigation  has  shown  that 
the  particular  alloy  known  as  manganin  is,  when  properly 
employed,  sufficiently  permanent  for  resistance  coils  and  resist- 
ance standards. 

The  composition  of  manganin  is  given  as  84  per  cent,  copper, 
12  per  cent,  manganese,  and  4  per  cent,  nickel.  Its  resistivity 
at  20°C.  is  about  44.5  microhms  (cm.)  and  its  thermo-electro- 
motive  force  when  opposed  to  copper  is  only  0.000002  volt  per 
degree  C.  To  insure  permanence  this  material  must  be  pro- 
tected by  a  well-dried  coating  of  shellac. 

The  curious  effect  of  a  rise  of  temperature  on  a  manganin 
resistance  coil  is  shown  in  Fig.  58.  The  point  at  which  the  tem- 
perature coefficient  changes  sign  varies  with  different  samples  of 
wire. 

It  will  be  noted  that  the  temperature  coefficient  is  very  small, 
the  average  value  between  15°C.  and  20°C.  being  only  0.0005 
per  cent.  For  engineering  work,  consequently,  temperature 
corrections  may  be  neglected.  In  work  of  the  highest  precision 
(a  few  parts  in  100,000)  temperature  corrections  must  be  made, 


130 


ELECTRICAL  MEASUREMENTS 


in  which  case  the  coefficient  applying  to  the  particular  coil 
hand  must  be  employed. 


in 


4000.45 
4000.40 
4000.35 
4000.30 

4000.25 
o 
|  4000.20 

'§4000.15 
K 
1 4000.10 

04000.05 
4000.00 


3999.00 


COIL,  4000   OHMS 


5°    18°  20°  22°  24°  26°  28°  30°  32°  34°  36C 
Degrees    Centigrade 


10°  12°  14W 
FIG.    58. — Showing  effect  of  temperature  on  a  manganin  resistance  coil. 


The  possible  effects  of  a  rise  of  temperature  on  a  resistance 
coil  are: 

1.  If  the  rise  of  temperature  is  small  there  will  be  a  temporary 
change  in  the  resistance;  that  is,  one  which  disappears  when  the 
normal  temperature  is  regained. 

2.  If  the   rise   of  temperature  is    great   there  will  be  a  per- 
manent alteration  of  the  resistance. 

3.  At  a  still  higher  temperature  the  insulation  will  be  impaired. 
It  is  evident  that  the  ability  of  a  resistance  coil  to  dissipate  the 

heat  due  to  the  passage  of  the  current  is  most  important,  and  as 
the  precisions  which  may  be  obtained  with  various  methods  of 
measurement  are  proportional  to  the  currents  employed,  it  is 
advisable,  when  selecting  a  resistance  box  for  general  use,  to 
choose  one  having  coils  of  a  high  watt  capacity. 

In  any  case  the  safe  working  current  is  that  which  will  heat  the 
coil  to  a  temperature  just  below  that  at  which  a  permanent 
alteration,  or  "set,"  in  the  resistance  will  take  place.  A  coil 
adjusted  to  0.01  per  cent.,  which  is  expected  to  maintain  this 
degree  of  reliability,  must  be  more  carefully  treated  than  one 
certified  to  0.05  per  cent,  which  is  a  degree  of  adjustment  fre- 


RESISTANCE  DEVICES  131 

quently  used  in  the  better  class  of  bridges  and  resistance  boxes 
for  general  use. 

No  definite  statement  can  be  made  as  to  the  safe  carrying,  or 
watt  capacity,  of  the  resistance  coils  used  in  boxes  for  general 
laboratory  work,  for  it  depends  on  the  construction  of  the  coils 
and  of  the  box  in  which  they  are  mounted  and  on  the  accuracy 
of  the  initial  adjustment  of  the  coils.  If  the  coils  are  of  good 
construction  and  wound  on  wooden  bobbins  0.5  watt  per  coil  may 
be  allowed.  If  metal  spools  in  metallic  connection  with  the  con- 
necting blocks  on  the  top  of  the  box  are  used,  3  watts  per  coil  is 
a  safe  allowance.  These  figures  are  for  coils  enclosed  in  wooden 
boxes  as  is  ordinarily  the  case.  If  many  coils  in  the  same  box 
are  simultaneously  used  lower  figures  must  be  employed. 

By  immersion  in  oil,  which  is  well  stirred,  the  watt  capacity 
of  a  coil  on  a  metal  bobbin  is  increased  to  about  7  watts. 

Standard  Resistances1. — Standard  resistances  are  used  for 
two  purposes: 

1.  As  standards  of  reference  with  which  other  resistances  are 
compared. 

2.  As   current   carrying   standards   for   use   in   potentiometer 
methods. 

With  the  first  class  of  coils,  permanence  is  all  important.  The 
watt  capacity  is  not  so  important  provided  it  is  great  enough  to 
allow  comparisons  to  be  made  with  the  desired  precision. 

Experience  has  shown  that  lack  of  permanence  in  the  finished 
coil  may  be  due  to  corrosion,  to  stresses  in  the  coil  owing  to  the 
fact  that  the  wire  is  wound  on  a  small  spool,  to  stresses  due  to 
the  absorption  of  moisture  by  the  insulating  materials,  and  to  the 
use  of  soft  solder  at  the  terminals  which  may  crack  and  alter  the 
effective  length  of  the  wire.  These  factors  are  now  generally 
recognized  and  the  coils  prepared  accordingly. 

For  coils  of  the  second  class,  a  high  carrying  capacity  is  abso- 
lutely necessary  and  one  can  tolerate  a  less  degree  of  permanence 
provided  comparisons  are  made  from  time  io  time  with  carefully 
preserved  resistance  standards;  as  a  matter  of  convenience  per- 
manence is  highly  desirable. 

The  designs  which  are  commonly  employed  for  resistance  stan- 
dards are  those  developed  at  the  Reichsanstalt,  Charlottenburg, 


132 


ELECTRICAL  MEASUREMENTS 


and  at  the  Bureau  of  Standards,  Washington.  Fig.  59  shows 
a  group  of  these  coils. 

For  standards  having  a  resistance  of  Jfo  ohm  and  greater,  the 
resistance  material  is  used  in  the  form  of  wire;  below  Ko  ohm, 
strips  are  employed. 

The  coils  are  kept  cool  by  immersion  in  oil.  Great  care  must 
be  taken  that  there  are  no  acids  or  sulphur  in  the  oil  and  that  it 


FIG.  59. — Standard  resistances. 

is  kept  free  from  water.  Otherwise  the  resistance  material  may 
be  attacked  and  the  accuracy  of  the  standards  impaired.  The 
oil  should  be  renewed  from  time  to  time. 

As  a  result  of  careful  experiments  at  the  Bureau  of  Standards 
it  has  been  found  that  coils  constructed  like  that  shown  at  A  in 
Fig.  59  are  subject  to  slight  variations  due  to  the  absorption  of 
moisture  by  the  shellac  used  in  insulating  the  windings.  This 


RESISTANCE  DEVICES  133 

swells  and  stresses  the  wire.  The  effect  is  most  noticeable  when 
fine  wires  are  used;  that  is,  in  high  resistance  coils.  It  follows 
the  seasonal-  variations  of  atmospheric  humidity,  and  may  be  as 
great  as  0.04  per  cent,  in  a  1,000-ohm  coil. 

Immersion  of  the  coil  in  oil  which  is  freely  exposed  to  the  air, 
though  retarding  the  effect,  is  not  an  absolute  preventive,  for 
the  oil  absorbs  moisture  and  imparts  it  to  the  shellac.  To  over- 
come this  source  of  error,  Rosa  has  developed  the  form  of  sealed 
resistance  standard3  shown  at  B  in  Fig.  59. 

The  coil  itself  is  prepared  as  specified  by  the  Reichsanstalt, 
being  insulated  with  silk  and  shellac  and  thoroughly  dried  by 
baking;  the  bobbin  is  supported  from  the  cover  by  the  thermome- 
ter tube.  The  case  is  nearly  filled  with  a  pure  oil  which  has 
been  carefully  freed  from  moisture.  The  cover  is  then  screwed 
into  the  protective  case  and  the  joint  sealed  with  shellac.  Poten- 
tial terminals  are  used  with  coils  of  1  ohm  or  less.  Sealed  stand- 
ard coils  show  no  seasonal  variations  in  resistance. 

Fig.  59C  shows  a  current-carrying  standard.  Such  resistances 
are  immersed  in  oil,  which  is  stirred  and  kept  cool  by  a  water 
jacket  through  which  there  is  a  brisk  circulation.  It  is  essential 
that  the  strips  of  resistance  material  be  protected  by  a  coating 
of  shellac. 

Resistance  Coils  for  Alternating-current  Work. — Though  the 
bifilar  winding  usually  employed  in  resistance  coils  reduces  the 
inductance  to  a  minimum,  it  increases  the  possibility  of  capacity 
effects,  since  at  the  terminals  of  the  coil  the  two  wires  are  separ- 
ated by  only  the  double  thickness  of  insulation  and  have  full 
voltage  between  them;  the  P.D.  between  the  wires  decreases 
with  the  increase  of  the  distance  from  the  terminals,  becoming 
zero  at  the  end  of  the  bight. 

It  is  clear  that  with  alternating  currents,  especially  at  high 
periodicities,  the  behavior  of  the  coil  will  be  modified  by  its 
distributed  capacity  and  inductance.  The  high  resistivity  of  the 
wires  eliminates  trouble  from  skin  effect,  which  at  3,000  cycles 
with  a  manganin  wire  2  mm.  in  diameter  is  only  about  1  part  in 
100,000. 

Assuming  as  an  approximation  that  the  formulae  for  two  paral- 
lel wires  apply  in  this  case,  Curtis  and  Grover  have  deduced  the 
following  relations7: 


134  ELECTRICAL  MEASUREMENTS 

Effective  resistance,  R'  =  R  [l  +  co2  C(  Y&L  -  ${5CR'2)]. 
Effective  inductance,  L'  =  L  -  %CR2. 

Phase  displacement,  tan"1  — ^~ -• 

/t 

R  and  L  are  the  total  resistance  and  inductance  of  the  coil  and 
C  is  the  capacity  between  the  wires  if  they  be  separated  at  the  end 
of  the  bight. 

It  is  seen  that  capacity  and  inductance  tend  to  neutralize  each 
other.  In  coils  of  low  resistance  with  only  one  layer  of  bifilar 
winding,  the  inductance  will  preponderate,  but  when  the  resist- 
ance of  the  coil  is  increased,  the  effect  of  capacity  increases  more 
rapidly  than  that  of  inductance;  consequently,  there  will  be  a 
point  where  the  two  effects  will  be  balanced.  The  balance  point 
is  practically  independent  of  the  frequency. 

From  the  formulae  it  is  evident  that  the  phase  displacement  and 
the  change  of  resistance  cannot  both  be  made  zero,  but  if  L  = 
HCR2  the  phase  displacement  is  zero  and  the  change  in  resist- 
ance negligible. 

After  having  found  a  construction  which  gives  a  practically 
non-reactive  coil,  higher  resistances  may  be  built  up  by  simply 
placing  coils  in  series.  The  several  sections  of  a  high-resistance 
coil  may  be  wound  side  by  side  on  the  same  spool  which  should 
be  of  porcelain.  The  use  of  a  non-conducting  spool  avoids 
troublesome  capacity  effects  between  the  sections. 

Curtis  and  Grover7  recommend  the  following  constructions: 

The  coils  are  designed  for  oil  immersion  and  have  approxi- 
mately 50  sq.  cm.  surface.  With  an  expenditure  of  1  watt  per 
coil  the  rise  of  temperature  above  the  surrounding  oil  is  about  1°, 
the  bobbin  being  of  poor  thermal  conductivity. 

Tenth-ohm  Coils. — Only  the  inductance  need  be  considered. 
The  coil  is  to  be  made  of  manganin  strip  ^{Q  mm.  thick,  width 
about  3  mm.,  length  about  10  cm.  The  strip  is  to  be  folded 
back  on  itself  at  the  middle  of  its  length  and  the  two  halves  bound 
together  with  insulation  between  them.  The  effective  inductance 
is  about  +0.005  microhenry. 

One-ohm  Coils. — Only  the  inductance  need  be  considered. 
The  coil  is  to  be  of  manganin  strip  J^o  mm-  thick  and  3  mm. 
wide,  folded  back  on  itself  at  the  middle  of  its  length,  and  with 


RESISTANCE  DEVICES  135 

proper  insulation  between  the  halves.     The  effective  inductance 
is  about  +0.05  microhenry. 

Ten-ohm  Coils.  —  Only  the  inductance  need  be  considered. 
Three  30-ohm  coils  are  used  in  parallel.  They  are  bifilar  wound 
on  spools  2.5  cm.  in  diameter,  a  single  layer  of  double  silk-covered 
manganin  wire  0.24  mm.  in  diameter  being  employed.  The 
effective  inductance  is  approximately  0.3  microhenry. 

One -hundred  ohm  Coils. — The  coils  are  bifilar  wound  in  one 
section,  a  single  layer  of  double  silk-covered  manganin  wire  0.24 
mm.  in  diameter  being  used.  The  capacity  effect  preponderates, 
resulting  in  an  effective  inductance  of  —1.6  microhenrys;  the 
phase  angle  at  2,000  cycles  per  second  is  about  35". 

One-thousand-ohm  Coils. — Five  sections,  each  of  two  hundred 
ohms,  are  used  in  series.  Each  section  consists  of  a  single  layer  of 
double  silk  covered  manganin  wire  0.10 
mm.  in  diameter.  The  five  sections  are 
bifilar  wound  on  a  spool  2.5  cm.  in  diam- 
eter, a  space  of  2  or  3  mm.  being  left  be- 
tween the  sections.  The  effective  induc- 
tance is  about  — 16.  microhenrys. 

Five -thousand -ohm  Coils. — Five  thou- 
sand-ohm coils  may  be  built  up  of  five  of 
the  above  1,000-ohm  coils  in  series  or  the 

bifilar  winding  may  be  replaced  by  that        FIG.  60. — Special 
.„    .  j  •     TI-      an  non-reactive  winding 

illustrated  in  Fig.  60.  for  high-resistance  coils. 

The  coil  is  wound  on  a  porcelain  cylin- 
der which  is  slit  along  a  diameter  for  about  two-thirds  of  its 
length.  Double  silk-covered  manganin  wire  is  used.  The  wire 
goes  once  around  the  bobbin,  then  passes  through  the  slit  and 
around  the  bobbin  in  the  opposite  direction  back  through  the 
slit.  This  cycle  is  repeated  until  the  whole  coil  is  wound.  The 
capacity  effect  is  very  small  as  there  is  only  a  small  P.D.  between 
adjacent  wires.  The  effective  inductance  is  about  +30.  micro- 
henrys. The  disadvantage  is  the  difficulty  of  winding. 

Ten-thousand-ohm  Coils. — These  are  constructed  'by  using 
in  series  two  of  the  5,000-ohm  units  just  described.  The  effective 
inductance  is  about  +100.  microhenrys. 

In  the  following  table  are  shown  comparative  results  given  by 


136 


ELECTRICAL  MEASUREMENTS 


the  above  coils  and  by  coils  as  ordinarily  supplied  by  representa- 
tive American  and  German  instrument  makers. 

TABLE  SHOWING  INDUCTANCE  EFFECTS  IN  RESISTANCE   COILS 


Nominal 

Effective  inductance  in  microhenrys  at 
1,200  cycles  per  second 

Change  in  resistance,  0  to 
1,200  cycles  per  second 

resistance 

of  coil, 

ohms 

New  coil 

American 

German 

New, 
per 
cent, 

American, 
per  cent, 

German, 
per  cent, 

0.1 

0.005 

0.14 

0.18 

1.0 

0.05 

0.4 

0.5 

10.0 

0.3 

0.9 

1.0 

100.0 

-1.6 

-5.0 

-2.0 

1,000.0 

-16.0 

-400.0 

-100.0 

<.001 

-0.08 

-0.05 

5,000.0 

30  0 

-27,500  0 

<.001 

-0  2 

10,000.0 

100.0 

-100,000.0 

<.001 

-1.0 

Micanite  cards  wound  with  resistance  wire,  such  as  are  used  for 
series  resistances  in  the  potential  circuits  of  alternating-current 


FIG.  61. — Showing  mounted  resistance  cards. 

instruments  are  highly  satisfactory  for  general  laboratory  pur- 
poses as  they  have  considerable  surface.  Capacity  effects  should 
be  minimized  by  mounting  the  cards  so  that  they  are  at  least  a 
centimeter  apart.  The  time  constant  of  one  of  these  cards  is 
10~6  to  10~7  second.  Duddell  and  Mather's  plan  of  weaving  a 
fine  wire  as  the  woof  in  a  silk  warp  gives  practically  the  same 
results  as  the  cards. 


RESISTANCE  DEVICES  137 

Low -resistance  Shunts  for  Use  in  Alternating-current  Meas- 
urements.— In  many  of  the  modern  methods  for  alternating- 
current  measurements,  for  instance,  those  for  determining  the 
ratios  and  phase  angles  of  current  transformers  and  for  measuring 
power  by  the  electrostatic  wattmeter,  "  non-inductive "  shunts 
having  large  carrying  capacities  are  employed. 

It  is  necessary  that  the  inductance  be  reduced  to  a  minimum, 
for  the  phase  displacement  between  the  current  and  the  P.D. 
at  the  shunt  terminals  must  be  as  small  as  possible  and  the  im- 
pedance must  be  sensibly  the  same  as  the  direct-current  re- 
sistance. Alsoj  when  the  inductance  is  reduced  to  a  minimum 
the  stray  field  and  therefore  the  disturbing  effect  on  neighboring 
instruments  is  correspondingly  decreased;  this  may  be  of  import- 
ance when  large  currents  are  dealt  with. 

If  low  resistances  are  employed,  the  amount  of  inductance 
which  can  be  tolerated  is  exceedingly  small.  For  instance,  at  60 
cycles  per  second  a  phase  displacement  of  0°.04  will  be  produced 
in  a  resistance  of  0.001  ohm  by  an  inductance  of  0.000000002 
henry  or  0.002  micjohenry  or  2  cm.  c.g.s.  At  low  power  factors 
even  this  inductance  is  of  importance  when  power  measure- 
ments are  made  with  the  electrostatic  wattmeter.  These  small 
inductances,  having  a  magnitude  of  only  a  few  centimeters,  can 
be  attained  only  by  special  care  in  design. 

As  such  low  resistances  are  for  use  with  large  currents  and  the 
voltage  drop  in  them  is  likely  to  be  considerable,  special  means 
must  be  provided  for  dissipating  the  heat  generated.  If  air 
cooling  is  relied  upon  the  shunt  becomes  bulky  and  expensive, 
so  it  is  generally  immersed  in  oil  which  is  violently  stirred  and 
is  kept  cool  by  a  water  jacket,  as  in  the  Reichsanstalt  form,5 
or  the  shunt  is  made  in  the  form  of  a  tube  through  which  water  is 
briskly  circulated,  as  in  that  designed  at  the  National  Physical 
Laboratory,  London.4 

Two  sizes  of  the  Reichsanstalt  shunts  are  shown  in  Fig.  62. 
They  are  made  according  to  a  suggestion  originally  due  to 
Ayrton.  A  single  thin  strip  of  manganin  is  doubled  back  on 
itself  at  the  middle  of  its  length,  and  the  two  parts  separated  by 
a  very  thin  layer  of  mica  insulation.  By  this  means  the  area  and 
consequently  the  flux  included  by  the  circuit  are  reduced  to  a 
minimum.  To  obtain  a  small  inductance  and  absence  of  skin 


138 


ELECTRICAL  MEASUREMENTS 


effect,  as  well  as  good  cooling,  the  strip  is  made  very  thin.  The 
potential  leads  are  brought  out  so  that  they  do  not  include  any 
flux  and  the  current  leads  are  strips  of  copper  with  very  thin 
insulation  between  them  so  that  they  set  up  no  appreciable  stray 
field. 

When  the  shunts  are  immersed  in  oil,  1  watt  per  square  centi- 
meter of  cooling  surface  is  allowed.     Of  course  only  one  side  of 


FIG.  62. — Low  -resistance  shunts  for  alternating-current  measurements. 
Designed  at  the  Reichsanstalt. 

the  sheet  is  effective  in  the  cooling.  The  thickness  of  the  mica 
insulation  between  the  leaves  is  from  0.1  to  0.3  mm.;  the  distance 
between  the  resistance  strips  is  from  0.2  to  0.5  mm.  In  the 
0.001-ohm  shunts  the  resistance  strip  is  69  cm.  long,  14.5  cm. 
wide  and  0.02  cm.  thick;  the  self-inductance  is  5.1  cm.  As  this 
resistance  is  intended  for  currents  up  to  1,000  amp.  the  loss  at 
full  load  is  1  kw. 

If  the  resistance  is  above  0.003  ohms,  the  construction  is  that 
shown  at  B  in  Fig.  62;  ze  and  zf  are  the  copper  current  leads. 


RESISTANCE  DEVICES 


139 


The  path  of  the  current  is  down  the  outside  strip  from  e  to  d, 
across  the  copper  connection  strip  k,  then  up  from  a  to  b  and 
down  to  c  across  k  to  g  and  up  to  the  terminal  b.  The  potential 
leads  are  attached  at  e  and  /.  Mica  insulation  is  used  between 
the  leaves  of  resistance  material. 

TABLE    OF    DATA    CONCERNING    OIL-COOLED    MANGANIN     RESISTANCES 
REICHSANSTALT  DESIGN  WITH  LEAVES  0.  5  MM.  APART 


Re- 

Breadth 

Length 

Thick- 

Nor- 

Volts 

Kw. 

Time 

Phase  dis- 

sist- 
ance, 

of 
strip, 

of 
strip, 

ness 
of  strip, 

mal 
current, 

drop  at 
normal 

nor- 
mal 

in 

constant 
L 

placement 
at  60 

ohms. 

cm. 

cm. 

mm. 

amp. 

current 

current 

R 

cycles 

0.03 

1.42 

51 

0.5 

40 

1.2 

0.048 

17.0 

5.7X10"7 

0°.012 

0.01 

3.6 

42 

0.5 

100 

1.0 

0.100 

5.8 

5.8X10"7 

0°.013 

0.003 

6.85 

49 

1.0 

333 

1.0 

0.333 

5.0 

17.0X10~7 

0°.036 

0.001 

14.5 

69 

2.0 

1,000 

1.0 

1.000 

5.3 

53.0X10"7 

0°.114 

The  effects  of  the  self-induction  of  a  '  \iunt  intended  for  use 
in  potentiometer  methods  may  be  compensated  by  mutual 
induction  between  the  shunt  and  the  potential  leads. 


a  & 


R,L. 
FIG.  63. — Compensation  for  shunt  inductance. 

Referring  to  Fig.  63,  at  balance  no  current  flows  in  the  voltage 
leads  to  a  and  b.  It  is  desired  to  make  the  potential  difference 
between  the  terminals  a  and  b  equal  to  and  in  phase  with  the 
ohmic  drop  in  R.  The  potential  difference  between  c  and  d  is 
shown  in  the  vector  diagram  by  VCd.  If  the  potential  leads  are 
arranged  so  that  there  is  mutual  induction  between  them  and 
the  main  part  of  the  shunt,  the  e.m.f.  induced  in  the  potential 
circuit  will  be  proportional  to  and  in  quadrature  with  the  current 
/  through  the  shunt. 

The  mutual  inductance,  w,  may  be  arranged  so  that  its  action 
either  aids  or  opposes  the  reactive  drop  in  the  shunt.  If  it  op- 
poses, then  the  P.D.  between  a  and  b  is  given  on  the  vector  dia- 
gram by  Vab,  and  if  the  mutual  inductance  be  adjusted  so  that 


140 


ELECTRICAL  MEASUREMENTS 


a  b 


m  =  L,  then  Vab  will  coincide  in  both  magnitude  and  direction 
with  IR]  that  is,  the  shunt  acts  as  if  it  were  non-reactive. 

This  method  of  obtaining  balance  of  inductances,  proposed  by 
A.  Campbell,4  is  indicated  in  Fig.  64. 

The  shunt  resistance,  R,  is  in  the  form  of  a  straight  strip  (or 
tube).  The  potential  leads  are  copper 
strips  of  the  same  width  as  the  main 
resistance.  They  are  carried  along  the 
body  of  the  shunt  to  about  the  middle 
of  its  length,  only  a  very  thin  layer  of 
RL  ~  insulating  material  being  interposed, 

FIG.  64.— A.  Campbell's  and  then  bent  perpendicularly  and  at- 
design    for    non-inductive 
shunt.  tached  to  the   potential  terminals,   a 

and  6.  By  this  means,  the  mutual  in- 
duction may  be  made  practically  to  balance  the  self-induction. 
The  balance  would  be  perfect  if  the  potential  leads  could  be 
made  coincident  with  R.  In  reality,  in  the  shunts  described 
below,  about  90  per  cent,  of  the  self-induction  effect  is  eliminated. 
In  carrying  out  this  scheme  of  construction  at  the  National 


FIG.  65. — Non-inductive  shunt.     Designed  at  National  Physical  Laboratory. 

Physical  Laboratory,  the  strip  has  been  replaced  by  a  manganin 
tube  enamelled  on  the  inside. 

The  tube  is  hard-soldered  to  hollow  copper  terminals  and  these 
in  turn  are  soft-soldered  to  the  current  leads,  which  are  carried 
back  parallel  to  the  tube,  to  about  the  middle  of  its  length,  where 


RESISTANCE  DEVICES 


141 


they  are  terminated  by  binding  posts,  This  cuts  down  the  stray 
field  of  the  shunt  itself  and  brings  the  current  leads  so  close  to- 
gether, that  their  field  has  little  effect  on  the  neighboring  appa- 
ratus. A  thin  copper  ring  is  hard-soldered  to  the  tube  at  the  mid- 
dle of  its  length.  When  the  shunt  is  used  in  connection  with  the 
electrostatic  wattmeter,  this  ring  is  used  as  a  terminal  (see  Fig. 
188). 

The  tube  is  covered  with  a  layer  of  varnished  cambric  about 
0.2  mm.  thick  and  outside  this  are  the  potential  leads,  in  the  form 
of  thin  sheaths  of  copper  foil  about  0.04  mm.  thick  extending 
from  the  ends  of  the  tube  to  near  its  middle,  where  they  are 
terminated  in  potential  posts. 

The  fluxes  which  produce  inductive  effects  are  those  in  the 
insulating  medium  between  the  tube  and  the  potential  leads  and 
in  the  main  tube  itself.  The  insualtion  therefore  should  be  as 
thin  as  practicable  and  the  potential  leads  should  very  closely 
surround  it.  The  resistance  tubes  should  be  very  thin  and  of 
large  diameter.  As  the  resistivity  is  high,  the  skin  effect  is 
negligible,  less  than  1  part  in  10,000  at  ordinary  frequencies. 
This  construction  reduces  the  effective  inductance  to  3  or  4  cm. 
or  to  0.003  or  0.004  microhenry. 

DATA  CONCERNING  WATER-COOLED  MANGANIN  RESISTANCES  DESIGNED 
AT  THE  NATIONAL  PHYSICAL  LABORATORY 


Re- 
sist- 
ance, 
ohms 

Out- 
-  side 
diam., 
mm. 

Thick- 
ness of 
wall, 
mm. 

Length, 
cm. 

Nor- 
mal 
cur- 
rent, 
amp. 

Max. 
cur- 
rent, 
amp. 

Volts 
drop  at 
normal 
current 

Kw.  at 
max. 
current 

L 

in 

cm. 

Time 
constant 
L 
R 

Phase  dis- 
placement 
at  60 
cycles 

0.04 

6 

0.25 

35W 

50 

115 

2 

0.53 

6.5 

1.6X10"? 

0°.003 

0.02 

10 

0.30 

40 

100 

260 

2 

1.35 

5.4 

2.7X10"? 

0°  .  006 

0.01 

15 

0.40 

39 

200 

450 

2 

2.00 

3.4 

3.4X10"? 

0°.007 

0.002      30 

1.00 

48 

1,000 

1,300 

2 

3.40 

3.7 

18.5X10"' 

0°.040 

0.001 

40 

1.5 

42^ 

2,000 

2,500 

2 

6.25 

3.0 

30.0X10"? 

0°.060 

To  obtain  a  high  carrying  capacity,  water  from  the  city  mains  is 
briskly  circulated  through  the  resistance  tube  at  a  rate  of  about 
15  liters  per  minute.  The  formation  of  a  layer  of  hot  water  in 
contact  with  the  resistance  material  is  prevented  by  a  centrally 
located  glass  rod  which  nearly  fills  the  tube.  For  the  same 
change  in  resistance  due  to  heating,  approximately  three  times 
as  much  energy  may  be  dissipated  as  when  simple  air  cooling  is 


142 


ELECTRICAL  MEASUREMENTS 


relied  upon.  As  much  as  10  kw.  may  be  dissipated  by  a  current 
of  3,000  amp.  in  a  tube  1^  in.  in  diameter  and  18  in.  long.  The 
current  density  may  be  as  great  as  16,000  amp.  per  square  inch. 
For  manganin  tubes,  up  to  1.5  mm.  thick,  10  watts  per  square 
centimeter  may  be  allowed  as  the  working  load. 

To  minimize  the  possibility  of  accidents,  this  form  of  resistance 
is  used  in  a  vertical  position,  the  water  inlet  being  at  the  bottom 
so  that  the  tube  is  always  filled. 

Resistance  Boxes. — Generally  speaking,  resistance  boxes  are 
constructed  so  that  the  resistance  between  their  terminals  may 
be  varied  from  zero  up  to  the  full  capacity  of  the  box  by  0.1  ohm 
or  by  1-ohm  steps.  This  must  be  accomplished  by  the  use  of  a 


JLrrA 


FIG.  66. — Diagram  show- 
ing series  arrangement  of  re- 
sistance coils. 


FIG.  67. — Connection  block 
for  resistance  box. 


moderate  number  of  coils.  A  common  arrangement  is  to  employ 
coils  of  1,  2,  2,  5  ohms,  with  similar  sets  for  the  tenths  and  the 
tens,  hundreds  and  thousands.  Another  possible  arrangement 
is  based  on  coils  having  the  denominations  1,  2,  3,  4.  The  coils 
are  so  mounted  that  any  desired  resistance  is  obtained  by  placing 
coils  in  series,  as  shown  in  Fig.  66.  The  drawing  of  a  plug  re- 
moves the  short-circuit  on  the  corresponding  coil.  The  current 
must  then  pass  from  the  terminal  block  through  the  coil,  and  on 
to  the  next  block. 

It  is  essential  that  the  top  of  a  resistance  box  be  very  rigid  in 
construction.  Consequently,  the  blocks  must  be  firmly  screwed 
to  the  vulcanite  top.  The  taper  of  the  plug  should  be  such 
that  a  good  contact  may  be  obtained  without  the  plug  becoming 
wedged  in  place.  The  blocks  should  be  undercut,  as  shown  in 
Fig.  67,  so  that  each  may  be  thoroughly  insulated  from  its 


RESISTANCE  DEVICES 


143 


neighbors.  Dimensions  which  have  been  found  satisfactory 
under  exceptionally  severe  service  are  shown  in  Fig.  67.  Each 
block  is  held  in  place  by  four  screws;  the  taper  of  the  plugs  is 
J-f  o  in.  per  1  in.  of  length. 

Dial  and  Decade  Arrangements. — A  common  dial  arrangement 
of  coils  employs  nine  1-ohm  coils,  nine  10-ohm  coils,  nine  100-ohm 
coils  and  so  on.  The  connections  are  such  that  any  number  of 
coils  in  any  set  may  be  put  in  series  with  any  other  set  or  sets. 
One  method  of  accomplishing  this  is  shown  in  Fig.  QSA.  A  single 
plug  is  used  in  each  dial. 


1000  w    Coils 

rilAAAl — LUAJ — UlAJ — LUAJ — LUAJ — LUAJ — LUAJ — LliAJ — LUAJ     I 

iynrtjTTyjTVT.^^ 


FIG.  68. — Dial  and  decade  connections  for  resistance  coils. 

A  great  disadvantage  of  this  particular  arrangement,  when 
plugs  are  used,  is  that  it  is  kept  clean  with  difficulty;  dust  and 
dirt  collect  on  the  hard  rubber  between  the  central  block  and  the 
coil  terminals  and  may  partially  short-circuit  the  coils,  especially 
those  of  high  resistance. 

Obviously  this  arrangement  lends  itself  readily  to  the  employ- 
ment of  a  rotative  switch  in  place  of  the  plug  for  connecting  the 
central  terminal  to  the  coil  terminals.  It  is  now  very  commonly 
used  and  when  the  switch  is  well  made  is  satisfactory  (see  Fig. 
93). 

Fig.  68J5  shows  a  decade  set,  which  is  the  equivalent  of  a  dial 


144 


ELECTRICAL  MEASUREMENTS 


arrangement,  but  with  the  coils  in  straight  lines.     This  greatly 
facilitates  keeping  the  top  of  the  box  clean. 

Multiple  Decade  Arrangements. — Instead  of  arranging  the 
coils  so  that  they  are  in  series,  they  may  be  put  in  multiple- if 
given  the  proper  values.  Fig.  68C  shows  such  an  arrangement. 


FIG.  69. — Feussner's  and  Smith's  decade  arrangements  of  resistance  coils. 

Let  the  highest  resistance  to  be  obtained  in  the  decade  be 
represented  by  A,  or  !%oA,  the  next  lower  step  is  %o^;  this  is 
to  be  obtained  by  placing  another  coil  in  parallel  with  the  first; 

by  figuring  the  parallel  circuits  it 
is  seen  that  the  second  coil  must 
have  a  resistance  of  9 A.  Simi- 
larly 
have 
4.2A, 
0.2A 
used. 


a 

the    remaining    coils   must 
resistances   of   7.2A,   5.6A, 
3.(U,    2.(U,    1.2A,    0.6A, 
and  0.     Ten  plugs  must  be 
This  arrangement  is  most 
advantageous  when  the  total  re- 
sistance  is  low,   for  the  compo- 
nent coils  have  higher  resistances 
and   are   therefore   more   readily 
adjusted  than  when  the  series  ar- 
rangement is  employed. 

Arrangements  for  Reducing 
the  Number  of  Coils  in  a  Dec- 
ade.— The  economical  disadvan- 
tage of  the  original  decade  ar- 
rangement lies  in  the  large  num- 
ber of  coils  which  must  be  made 
and  adjusted;  several  alternative 
arrangements  are  shown  above. 

In  Feussner's  decade  arrangement,  which  gives  resistances 
from  0  to  9  units,  the  first  four  coils  are  arranged  as  in  the  ordi- 
nary decade  system;  the  fifth  value  is  obtained  by  using  a  single 


FIG.    70. — Northrup's   decade   ar- 
rangement for  resistance  coils. 


RESISTANCE  DEVICES 


145 


coil  of  5  units  and  the  succeeding  values  by  employing  this  coil 
in  series  with  the  four-step  decade.  Only  one  plug  is  required. 

The  difference  between  Smith's  and  Feussner's  arrangements 
is  obvious. 

In  Northrup's  arrangement,  four  coils  having  denominations 
1,  3,  3,  2,  units  are  used.  In  Fig.  70,  I,  II,  III,  IV,  V,  are  termi- 
nal posts  and  taps  which  may  be  connected  as  desired.  If  all  the 
coils  are  used  in  series  the  resistance  is  9  units.  The  other  values 
are  obtained  as  shown  below. 


Points  to  be  connected 

Resistance  between  term- 
inals I  and  V 

Units 

I—  V 

0 

II—  V 

1 

IV—  I 

2 

II—  IV 

3 

III—  V 

4 

I—  III 

5 

II—  III 

6 

IV—  V 

7 

I—  II 

8 

The  construction  necessary  for  carrying  out  this  scheme  by  the 
use  of  a  single  plug  is  shown  in  Fig.  70. 


RHEOSTATS 

Water  Rheostats. — To  control  a  small  current  and  to  be  able 
to  give  it  any  value  between  zero  and  a  maximum,  the  arrange- 
ment shown  in  Fig.  71  may  be  used. 

The  compensating  cell  renders  it  possible  to  bring  the  current 
in  the  derived  circuit  smoothly  down  to  zero.  If  the  cell  is  not 
used,  there  will  be  a  sudden  change  in  the  current  when  the 
electrodes  a  and  b  are  brought  into  contact. 

Water  rheostats  are  commonly  used  for  absorbing  energy 
during  tests  of  electrical  machinery.  The  "  water  barrel," 
shown  in  Fig.  72,  is  convenient  when  small  amounts  of  power  are 
to  be  dealt  with. 

A  stout  wooden  barrel  is  used.     An  ordinary  cast-iron  stove 
10 


146 


ELECTRICAL  MEASUREMENTS 


grate  about  15  in.  in  diameter  is  placed  at  the  bottom  of  the 
barrel  and  provided  with  a  terminal  of  insulated  wire.  A  second 
grate,  S',  is  screwed  to  an  iron  rod  and  suspended  by  a  rope  which 
passes  over  pulleys  to  a  counterweight.  Short  wooden  pegs 
prevent  the  two  grates  from  being  brought  into  contact.  Fresh 
water  is  used  and  the  required  conductivity  obtained  by  adding 
a  salt,  such  as  sodium  carbonate. 

Such  a  " water  barrel"  will  take  about  25  amp.  at  2300  volts, 
absorbing  about  100  kw.;  the  water  will 
boil  violently  when  the  rheostat  is 
forced  to  this  extent.  An  adequate 
water  supply  must  be  provided  and 
arrangements  made  by  which  the  bar- 
rel may  be  kept  full  without  danger 


Compensating 
Cell 


FIG.  71. — Water  rheostat  for  small 
currents. 


FIG.    72. — Water-barrel 
rheostat. 


to  the  operator.     On  account  of  the  steam  and  gases,  such  rheo- 
stats should  be  used  out-of-doors. 

When  rheostats  of  this  general  form  are  used,  there  is  always 
more  or  less  slopping  over  of  the  water.  The  ground  and  sur- 
rounding objects  often  become  thoroughly  saturated  and  the 
greatest  care  must  be  exercised  by  the  attendants  that  severe  or 
perhaps  fatal  shocks  are  not  experienced  through  inadvertantly 
touching  some  of  the  wiring:  One  must  not  relax  his  vigilance 
because  the  voltage  is  low,  for  with  sufficiently  good  contacts, 
shocks  from  110- volt  circuits  have  proved  fatal.  The  station 
for  the  operator  should  be  properly  raised  from  the  ground, 
so  that  the  platform  will  be  dry  and  the  ropes  by  which  the  elec- 
trodes are  manipulated  should  be  rendered  safe  by  the  intro- 
duction of  strain  insulators. 


RESISTANCE  DEVICES 


147 


Water  Rheostats  with  Plate  and  Cylindrical  Electrodes. — In 
case  there  is  a  running  stream  or  open  canal  of  fresh  water  near 
the  station  and  the  voltage  is  high,  the  forms  of  rheostat  shown  in 
Figs.  73  and  74  are  convenient. 

That  shown  in  Fig.  73  was  used  for  absorbing  power,  up  to  700 
kw.,  in  a  2,300-volt  three-phase  circuit.  There  are  three  terminal 
and  four  neutral  plates  spaced  4  in.  apart  on  centers,  all  of  iron, 
the  dimensions  being  60  in.  by  24  in.  by  J^  in.  The  frame  is 


FIG.  73. — Three-phase  power-absorbing  rheostat  with  plate  electrodes. 


hung  by  a  tackle  so  that  the  amount  of  power  may  be  regulated 
by  varying  the  immersed  area.  For  these  immersion  rheostats 
the  allowable  current  density  at  the  electrodes  is  about  3.5 
amperes  per  square  inch. 

In  the  rheostat  shown  in  Fig.  74,  which  is  also  designed  for 
three-phase  loading,  a  wooden  frame  made  in  the  form  of  an 
equilateral  triangle  is  provided.  The  three  vertical  electrodes 
are  of  thin  metal  pipe  and  are  connected  by  flexible  cables  to  the 


148 


ELECTRICAL  MEASUREMENTS 


leads  so  that  the  frame  may  be  raised  or  lowered  by  means  of  a 
tackle  and  the  immersion  of  the  electrodes  varied. 

If  the  conductivity  of  the  water  is  known,  the  rheostat  may 
be  designed  to  absorb  a  given  amount  of  power.  The  arrange- 
ment of  electrodes  is  shown  in  Fig.  75. 


FIG.  74. — Three-phase  power-absorbing  rheostat  with  cylindrical  electrodes. 

The  electrostatic  capacity  of  two  parallel  cylinders  in  air, 
diameter  D  cm.,  spaced  a  cm.  on  centers,  length  I  cm.  is  * 


C  = 


I 


4  log. 

a  +  * 

V/a2 

-  D2 

D 

(21 
^ 


Hence,  the  conductance  between 
these  cylinders  when  immersed  in  an 
infinite  medium  of  conductivity  p'  will 
be 


FIG.  75. — Arrangement  of 
electrodes  in  three-phase 
water  rheostat. 


D 


then 


Q  = 


1.36p'Z 


RUSSELL,  "Alternating  Currents,"  vol.  1,  p.  102. 


RESISTANCE  DEVICES 


149 


The  current  which  will  flow  between  two  parallel  cylindrical 
electrodes  when  they  are  immersed  in  a  great  body  of  liquid  is 

IMp'lE 


and  the  power  absorbed  is 
P  = 


(1) 


\oglo{K  +  VK*-  i 


WATER  RHEOSTAT  WITH  PARALLEL  CYLINDRICAL  ELECTRODES 
Length  in  Cm. 

Conductivity,   P,  in  Mho,  Cm. 
Three  Phase  Single  Phase 


32 


FIG.  76. — Showing  constants  of  water  rheostat  with  different  spacings  of 
cylindrical  electrodes. 

In  the  case  of  a  three-phase  rheostat  the  line  current  will  be 


J.  £,     —  / —    J.  —       J..J.C/J. 

\/3 
and  the  power  absorbed  will  be  given  by 


P  = 


2.72p'lE* 


logic  (K 


The  conductivity,  p',  which  is  greatly  influenced  by  local 
conditions  and  by  temperature,  must  be  found  for  the  water  which 
is  to  be  used.  To  determine  it  two  conducting  cylinders  of  a 
known  diameter  may  be  fixed  at  a  known  distance  apart  and  the 
arrangement  immersed  in  the  running  water.  A  measured 


150 


ELECTRICAL  MEASUREMENTS 


alternating-current  voltage  is  then  applied  between  the    two 

cylinders  and  the  resulting  current  determined,     p  is  calculated 

by  aid  of  (1). 

Wire -wound  Rheostats. — For  general  laboratory  purposes,  a 

very  convenient  rheostat  adapted  to  low  voltages  is  shown  in 

Fig.  77. 

The  upright  frame,  6  ft.  high  and  3  ft.  wide,  is  strung  with  about 

550  ft.  of  bare  lala  wire,  contained 
in  100  sections.  When  110  volts  is 
applied  at  the  terminals  of  the  frame, 
one  can,  by  means  of  spring  clips,  tap 
off  voltages  or  small  currents.  By 
means  of  four  clips  and  flexible  con- 
nection wires,  the  arrangement  may 
be  divided  into  sections  and  these 
connected  in  parallel. 

A  cheap  and  convenient  form  of 
rheostat,  which  has  proved  very  use- 
ful for  loading  the  small  generators 
used  for  purposes  of  instruction  in 
electrical  engineering  laboratories  is 
shown  in  Fig.  78. 

The  wire  is  wound  in  screw-threads 
on  moulded  porcelain  cylinders. 
These  cylinders  are  loosely  held  in 
place  on  the  angle-iron  frame  in  such 

a  manner  that  they  may  be  readily 
FIG.  77.-Resistance  frame.      removecL      The    base    and    the    top> 

which  carries  the  switches,  are  of  " ebony  asbestos  wood."     The 
following  sizes  of  lala  wire  have  been  employed: 


Size  of  wire 

No.  17 
No.  20 
No.  26 
No.  23 


Full  load  capacity 

104  amp.  at  110  volts 
52  amp.  at  110  volts 
20  amp.  at  220  volts 
40  amp.  at  220  volts 


Immersed-wire  Rheostats. — The  carrying  capacities  of  wires 
may  be  greatly  increased  by  immersing  them  in  water,  as  will  be 
seen  from  the  following  table  giving  approximate  data  concerning 
galvanized-iron  wire.  Immersed  rheostats  are  useful  in  tempo- 


RESISTANCE  DEVICES 


151 


rary  arrangements  of  apparatus.  Fine  wires  may  be  corroded  off 
after  a  short  time.  Provision  must  be  made  for  safely  replacing 
the  water  lost  by  boiling. 

TABLE  OF  APPROXIMATE  DATA  CONCERNING  CARRYING  CAPACITY  OF 
GALVANIZED-IRON  WIRE  WHEN  IMMERSED  IN  WATER 


No. 
B.  &S. 

In  air 

In  water 

Circular 
mils 

Amperes 

Ft.    per 
110  volts 

Amperes 

Ft.    per 
110  volts 

Ft.    per 
550  volts 

Ft.  per 
Ib 

20 

1,018 

2.5 

594 

36 

25 

125 

369.0 

19 

1,253 

2.9 

626 

42 

27 

135 

293.0 

18 

1,624 

3.5 

673 

50 

29 

145 

232.0 

17 

2,048 

4.2 

710 

60 

-30 

150 

184.0 

16 

2,583 

5.0 

750 

71 

32 

160 

246.0 

15 

3,257 

6.0 

790 

88 

34 

170 

107.0 

14 

4,107 

7.1 

840 

103 

36 

180 

91.9 

13 

5,178 

8.5 

886 

122 

38 

190 

72.1 

12 

6,530 

10.1 

941 

145 

40 

200 

57.8 

11 

8,234 

12.0 

990 

173 

42 

210 

45.8 

10 

10,380 

14.3 

1,054 

205 

45 

225 

36.4 

9 

13,090 

17.1 

1,103 

245 

47 

235 

33.3 

8 

16,510 

20.3 

1,354 

293 

49 

290 

25.0 

The  heating  of  these  wires  when  immersed  is  so  great  that 
there  must  be  no  obstruction  to  a  free  circulation  of  the  cooling 
water.  Strong  strings  or  fairly  sharp  edges  of  wooden  sticks 
will  make  reliable  supports.  The  water  used  must  be  clean, 
to  prevent  rapid  destruction  of  the  wires  by  electrolysis. 

Drop  Wires. — A  very  useful  form  of  drop  wire  for  controlling 
the  voltages  applied  to  the  potential  coils  of  instruments  may 
be  made  by  winding  a  single  layer  of  double  cotton-covered 
resistance  wire  on  a  piece  of  brags  tube  about  a  meter  long  and  5 
cm.  in  diameter,  which  has  been  slit  lengthwise  and  covered  with 
stout  paper.  The  insulation  is  sandpapered  off  where  the  slider 
makes  contact.  By  use  of  this  device,  the  voltage  in  a  derived 
circuit  may  be -adjusted  from  zero  to  a  maximum.  It  should 
not  be  forgotten  that  the  arrangement  is  a  long  solenoid  and  will 
have  a  considerable  stray  field. 

Rheostats  similar  to  those  shown  in  Fig.  79  are  regularly  on 
the  market,  and  are  very  convenient  for  general  laboratory  pur- 


152 


poses.     In  the  G.R.   type 
wound  on  slate  blocks. 


ELECTRICAL  MEASUREMENTS 

the    constantin    resistance    wire  is 


FIG.  78. — Laboratory  rheostat  for  loading  small  generators. 


FIG.  79. — Slide-wire  rheostats  for  small  "currents. 

There  are  numerous  stock  forms  of  rheostats  which  may  be 
obtained  from  the  electrical  manufacturing  companies  and  which 
are  useful  in  particular  cases. 


RESISTANCE  DEVICES 


153 


Carbon  Compression  Rheostats. — Carbon  compression  rheo- 
stats are  exceedingly  useful  as  laboratory  appliances  where 
low-voltage  currents  are  to  be  controlled — as,  for  example,  in 
calibration  work. 

The  essential  feature  is  a  series  of  specially  moulded  carbon 
plates,  which  can  be  forced  into  more  or  less  intimate  contact  by 
a  screw. 

A  convenient  form  of  carbon  compression  rheostat  is  shown  in 
Fig.  80.  It  contains  90  plates  each  1%  in.  by  IJ^  in.  by  %  in. 

A  4-volt  current  can  be  controlled  between  the  limits  1  and  28 
amp.,  the  resistance  of  the  circuit  outside  the  rheostat  being  0.1 
ohm. 


FIG.  80. — Carbon  compression  rheostat. 


References 

1.  "Resistance  Coils  and  Comparisons,"  (shows  various  forms  of  construc- 
tion), C.  V.  DRYSDALE,  The  Eectrician,  vol.  59,  1907,  pp.  955,  989,  1035. 

2.  "Alloys  for  Resistance  Coils,"  ST.  LINDECK,  The  Electrician,  vol.  30, 
1893,    p.    119.     "tJber   die    Haltbarkeit   von    Kleinen    Widerstande    am 
Manganene    Bleck   im    Praktischen    Gebrauch,"    ST.    LINDECK,    Zeit.   fur 
Instrumentenkunde,  vol.  23,  1903,  p.  1. 

3.  "The  Variation  of  Resistances  with  Atmospheric  Humidity,"  E.  B. 
ROSA  and  H.  D.  BABCOCK,  Bulletin  of  the  Bureau  of  Standards,  vol.  4, 
1907-08,  p.  121.     "A  New  Form  of  Standard  Resistance,"  EDWARD  B.  ROSA, 
Bulletin  of  the  Bureau  of  Standards,  vol.  5,  1908-09,  413. 

4.  "Non-inductive    Water-cooled   Standard    Resistances    for    Precision 
Alternating-current  Measurements,"  CLIFFORD  C.  PATTERSON  and  E.  H. 
RAYNER,  Journal  Institution  of  Electrical  Engineers,  vol.  42,  1908-09,  p.  455. 
"On  Compensation  for  Self-inductance    in   Shunt   Resistances,"  ALBERT 
CAMPBELL,  The  Electrician,  vol.  61,  1908,  p.  1000. 

5.  "Uber  Starkstromwiderstande  mit  Kleine  Selbsinduktion,"  E.  ORLICH, 
Zeit.  fiir  Instrumentenkunde,  vol.  29,  1909,  p.  241. 


154  ELECTRICAL  MEASUREMENTS 

6.  "The  Measurement  of  the  Inductances  of  Resistance  Coils,"  Frederick 
W.  GROVER  and  Harvey  L.  CURTIS,  Bulletin  Bureau  of  Standards,  vol.  8, 
1912-13,  p.  455. 

7.  "Resistance    Coils  for   Alternating-current   Work,"    FREDERICK   W. 
GROVER  and  HARVEY  L.  CURTIS,  Bulletin  of  the  Bureau  of  Standards, 
vol.  8,  1912,  p.  495  (see  also  p.  455  as  above). 

8.  "The  Water  Rheostat  as  an  Artificial  Load  for  Electric  Installations," 
E.  A.  EKERN,  Stone  &  Webster  Public  Service  Journal,  vol.  9,  1911,  p.  312. 


CHAPTER  IV 
THE  MEASUREMENT  OF  RESISTANCE 

Volt  and  Ammeter  Method. — The  most  obvious  method  of 
determining  an  electrical  resistance  is  by  the  direct  application  of 
Ohm's  law.  The  potential  difference  between  the  terminals  of 
the  resistor  and  the  current  flowing  through  it  are  measured  by 
appropriate  instruments,  which  have  previously  been  calibrated. 

It  is  important  not  to  lose  sight  of  the  possible  influence  of  the 
measuring  instruments  on  the  results.  With  the  terminal  at  1 
(Fig.  81)  the  voltmeter  gives  the  proper  potential  difference,  but 
the  ammeter  measures  the  current  through  the  unknown  resist- 
ance plus  that  through  the  voltmeter.  If  the  resistance,  X,  be  at 
all  comparable  with  that  of  the  voltmeter,  the  error  may  be  great 
unless  allowance  be  made  for  the  voltmeter  current.  In  this 


x — s       ^_ g >. 


FIG.  81. — Volt  and  ammeter  method  for  measuring  resistance. 

case  the  voltmeter  resistance  must  be  known.  If  the  terminal  be 
at  2,  the  ammeter  gives  the  proper  current  but  the  measured 
potential  difference  includes  the  drop  in  the  ammeter  and  its 
connections;  if  this  be  an  appreciable  fraction  of  that  in  X,  the 
error  will  be  large  unless  this  drop  is  subtracted  from  the  volt- 
meter reading.  These  considerations  should  be  given  weight  when 
making  connections  for  any  particular  test. 

If  the  voltmeter  be  of  low  resistance,  care  must  be  taken  that 
the  resistances  of  the  leads  and  contacts  are  negligible.  The  volt- 
ammeter  method  finds  frequent  employment  in  emergency  work 
where  comparatively  rough  measurements  will  suffice;  for 
instance,  in  determining  armature  resistance. 

155 


156  ELECTRICAL  MEASUREMENTS 

Substitution  Method. — This  method  is  based  on  the  assump- 
tion that  the  e.m.f.  and  resistance  of  the  battery  employed  are 
constant. 

With  the  connections  as  in  Fig.  82  the  galvanometer  current  is 


If,  by  means  of  a  switch,  S  be  substituted  for  X  and  adjusted 
until  the  deflection  is  the  same  as  before,  then  obviously 

S  =  X. 

Any  error  which  might  be  due  to  the  law  of  deflection  of  the 
galvanometer  is  eliminated.     The  shunt  Rs  serves  to  vary  the 


X 


< — s— 

I —  * 


FIG.  82. — Substitution  method  for  measuring  resistance. 

sensitivity  of  the  galvanometer  to  suit  different  conditions.  The 
resistances  of  the  other  parts  of  the  circuit  should  be  small  com- 
pared with  S  and'X;  for  this  reason  arrangements  should  be 
made  so  that  the  number  of  battery  cells  may  be  varied.  The 
substitution  method  in  a  modified  form  is  frequently  used  in 
dealing  with  very  high  resistances  (see  ''Insulation  Resistance"). 

Direct-deflection  Method. — Two  resistors  which  are  to  be 
compared  may  be  connected  in  series  and  the  potential  differ- 
ences between  their  terminals  measured  by  voltmeters  of  the 
proper  range.  If  the  current  be  constant,  a  single  instrument 
may  be  used;  its  deflection  should  be  proportional  to  the  current 
and  it  should  be  so  arranged  that  the  terminals  can  be  quickly 
transferred  from  S  to  X,  see  Fig.  83. 

R  is  a  variable  resistance  for  changing  the  range  of  the  volt- 
meter; if  the  current  taken  by  the  voltmeter  be  negligible, 


_  <??*  (Rv  +  Rx\ 

f>        \  7?        i      f>     J 

LJ <2       \  £vv    ~T~    £La' 


THE  MEASUREMENT  OF  RESISTANCE         157 

Dx  and  Ds  are  the  readings,  and  Rx  and  Rs  the  resistances 
unplugged  in  R  when  the  terminals  are  on  X  and  on  S  respec- 
tively. RV  is  the  voltmeter  resistance.  If  the  current  fluctuates, 
two  voltmeters  should  be  used,  simultaneous  readings  being 
taken  by  two  observers.  This  procedure,  millivoltmeters  being 
employed,  is  frequently  used  for  testing  rail  bonds  in  situ;  the 
resistance  of  a  given  length  of  rail  including  a  bond  being  com- 
pared with  that  of  the  same  length  without  a  bond.  The  volt- 
ages measured  are  those  due  to  the  return  current  through  the 
rail. 

Potentiometer  Method. — Instead  of  determining  the  potential 
difference  between  the  terminals  of  S  and  of  X  by  a  voltmeter, 
the  potentiometer  (see  page  271)  may  be  used.  Obviously  the 


V.M. 


FIG.  83. — Direct  deflection  method  for  measuring  resistance. 

current  in  S,  in  X  and  that  in  the  potentiometer  must  remain 
constant  during  the  test.  As  the  processes  of  balancing  and 
checking  the  constancy  of  the  potentiometer  current  require  some 
time,  this  condition  is  very  difficult  of  practical  realization;  while 
the  method  may  be  made  to  give  accurate  results,  the  measure- 
ment becomes  a  time-consuming  operation.  In  very  accurate 
measurements,  the  possibility  of  a  heating  error  is  considerable, 
for  the  current  must  be  kept  on  continuously  during  the  process 
of  balancing. 

In  order  that  resistances  may  be  determined  with  accuracy  and 
despatch,  it  is  necessary  to  have  methods  which  are  independent 
of  fluctuations  of  the  testing  current.  Such  methods  will  now  be 
discussed. 

Differential-galvanometer  Method. — A  differential  galva- 
nometer has  two  distinct  windings  which  are  thoroughly  insulated 
from  each  other,  of  equal  magnetic  strength,  of  equal  resistance, 
and  as  nearly  coincident  as  possible.  To  attain  these  conditions 


158  ELECTRICAL  MEASUREMENTS 

the  wires  are  wound  throughout  their  length  side  by  side  and  in 
layers.  Any  residual  magnetic  effect,  if  the  instrument  be  of  the 
Kelvin  type,  may  be  annulled  by  a  small  coil  placed  outside  the 
case  of  the  instrument  and  connected  in  series  with  the  weaker 
coil  in  such  a  manner  that  its  effect  is  additive;  this  adjusting 
coil  is  mounted  so  that  its  position  may  be  altered  by  sliding  it 
along  a  rod  which  is  coaxial  with  the  main  coil. 

The  simplest  method  of  using  the  instrument  is  shown  in 
Fig.  84. 

On  the  diagram  RGx  and  RGa  are  the  resistances  of  the  two  gal- 
vanometer coils;  Lx  and  Ls  the  total  lead  resistances;  Rx  and  Ra 
the  resistances  unplugged  in  the  boxes.  To  avoid  leakage  and 
capacity  effects,  the  positions  of  the  boxes  Rx  and  Rs  should  be 
such  that  the  potential  difference  between  the  two  galvanometer 


M>^ 


FIG.  84. — Simple  method  of  usino;  d  inferential  galvanometer. 

coils  is  a  minimum.     The  resistance  of  a  should  be  low.     High 
insulation  of  the  leads,  etc.,  is  necessary. 

First,  the  adjustment  of  the  instrument  must  be  tested.  To 
do  this  the  coils  are  connected  in  series  and  opposed  magnetically ; 
the  maximum  working  current  is  then  sent  through  them.  No 
deflection  should  be  observable.  Perfect  adjustment  is  obtained 
by  adjusting  the  auxiliary  coil. 

With  the  connection  shown  in  Fig.  84,  after  having  unplugged 
a  suitable  resistance  in  Rx,  the  value  of  Rs  is  adjusted  until  the 
galvanometer  stands  at  zero;  then  the  currents  in  the  two  coils  are 
equal,  and 

X      RGx  +  Rx  +  Lx  +  X 
S  ''''  RG,  +  RS  +  LS  +  S 

or  X  =  S  R°x  "*"  Rx  "*"  Lx 

RGf  +  Rs  +  Ls 

The  galvanometer  and  lead  resistances  must  be  known. 


THE  MEASUREMENT  OF  RESISTANCE         159 

An  alternative  method  is  to  unplug  a  small  resistance,  Rx,  and 
obtain  a  balance,  by  adjusting  Rs,  then  to  make  Rx  large  and 
repeat  the  balance.  If  all  other  resistances  remain  constant,  and 
the  values  unplugged  be  Rx,  R'x,  and  Rs,  R'a, 

e  R'x  —  Rx 

=  *          ' 


The  differential  galvanometer  was  formerly  in  quite  common 
use  but  was  supplanted  by  the  Wheatstone  bridge.  Of  late  years, 
however,  the  instrument  has  again  come  into  use  for  measure- 
ments where  the  range  to  be  covered  is  not  large,  for  instance  in 
resistance  pyrometry  and  in  the  comparison  of  nominally  equal 
resistances. 

A  practical  difficulty  is  that  the  exact  adjustment  of  a  sensitive 
instrument  is  somewhat  troublesome  and  when  made  is  not  per- 
manent, being  subject  to  changes  in 
the  levelling  of  the  galvanometer. 
Therefore,  methods  have  been  sug- 
gested where  the  deflection  is  not 
brought  exactly  to  zero.1 

Kohlrausch  Method  of  Using  a 
Differential  Galvanometer.2  —  For 
work  of  the  highest  class,  such  as  the 

precision     comparison     of     resistance 

•,      i      ,!  ,11  i         i  FIG.    85.  —  Diagram    for 

standards,  the  method  employed  must  Kohlrausch    method     of 

be  free  from  errors  due  to  variations  using  a  differential  galva- 
in  the  resistances  of  the  galvanometer 

circuits.  These  might  be  caused  by  changes  of  connections, 
involving  the  alteration  of  contact  resistances,  or  they  might  be 
due  to  the  inclusion  of  potential  terminals  of  the  resistances 
during  the  test  but  not  when  making  the  preliminary  adjustment 
for  differentiality. 

Kohlrausch's  method  of  overlapping  shunts  fulfils  the  desired 
conditions.  It  is  designed  for  the  comparison  of  nominally 
equal  resistances.  The  scheme  of  connections  is  shown  in  Fig. 
85.  In  carrying  out  the  test  some  means  of  adjusting  either  S 
or  X,  as  well  as  one  of  the  galvanometer  circuits,  is  required. 

It  is  also  necessary  to  be  able  to  interchange  B  and  a  (equiva- 
lent to  interchanging  the  galvanometer  circuits  A  and  C).  This 


160 


ELECTRICAL  MEASUREMENTS 


Position 


Position 


may  conveniently  be  done  by  a  commutator  with  mercury  con- 
tacts such  as  is  shown  in  Fig.  86.  The  parts  L  are  insulating 
strips  of  ebonite;  the  other  parts  of  the  rocker  are  of  copper; 
two  middle  arcs  are  in  electrical  connection. 

The  parts  of  the  commutator  are  so  large  that  the  resistance 

of  the  circuit,  and  therefore  the  bat- 
tery current,  is  not  appreciably  altered 
by  the  interchange. 

Referring  to  Fig.  87,  N  is  a  shunt. 
A  good  resistance  box  may  be  used; 
in  practice  it  is  applied  to  the  larger 
86.  — Commutator  of  the  twQ  resistances,  S,  X.  By  "it, 
the  resistance  between  3  and  4  is  re- 
duced to  equality  with  that  between 

1  and  2.  The  resistance  of  one  of  the  galvanometer  circuits  is 
adjusted  by  means  of  g  and  n]  trial  determines  which  one  should 
be  varied. 

As  S  and  X  are  supposed  to  be  nearly  equal,  the  galvanometer 
is  made  as  nearly  differential  as  convenient  but  need  not  be 
exactly  adjusted.  *' 

AC  AC 


FIG. 

for  interchanging  the  galva- 
nometer coils. 


Rh  Rh 

Position  I  Position  II 

FIG.  87. — Showing  connections  for  both  positions  of  the  commutator  in 
Kohlrausch  method. 

The  connections  for  the  two  positions  of  the  commutator  are 
shown  in  Fig.  87. 

In  order  to  find  the  conditions  necessary  for  balance,  the  galva- 
nometer deflections  for  the  two  positions  of  the  rocker  must  be 


THE  MEASUREMENT  OF  RESISTANCE 


161 


determined.  Let  the  connections  be  as  shown  in  Fig.  88..  The 
resistances  of  the  various  circuits  are  indicated  on  the  diagrams; 
«6  and  i&  are  the  galvanometer  currents,  IB  the  battery  current. 
Let  Si  be  the  resistance  between  3  and  4;  with  the  connections 
shown  in  the  diagram,  it  is  the  parallel  resistance  of  S  and  N 
(Fig  87). 

n(r6  +  a  +  X)  -  iB(X  +  a)  +  i6a  =  0. 

ibfa  +  a  -h  Si)  —  IB(OL  +  Si)  +  i&a  =  0. 

i'efo  +  Si  +  a')  -  ^(Si  +  a')  +  ;'Ba'  =  0. 

i'*(r*  +  X  +  a/)  -  i'*(X  +  a')  +  *'««'  =  0. 


Position   1  Position  II 

FIG.  88. — Mesh  diagram  for  Kohlrausch  method. 
Solving  for  the  desired  currents  and  letting 

M  '~=  *(r* + r6  +  St  +  x)  VinT+'SiX^  + ~x) 

*'_ 

M'    =    -77 


+  (r5  +  Z)(ra  +  Si) 


a,  +  r6  +  Si 
M{a(r6  +  X) 


Now  let  the  deflection  per  ampere  due  to  the  coil  carrying  ib 
be  A  and  that  for  the  coil  carrying  z'6  be  B.  Then,  as  the  two  coils 
oppose  each  other  and  their  effects  are  very  nearly  equal,  the 
resultant  deflection  will  be 

For  position  /, 
Dj  =  M[A{a(r6+Si)+Si(rs+X)}-B{a(r6+X)+X(n  +  Si)}]. 

For  position  //, 
DII  =  M'[A{a'(rG+X)+X(r&+Si)}-B{a'(rb+Si)+Sl(rb+X)}]. 

Conditions  for  Balance.  —  Suppose  that  by  adjusting  the  resist- 
ances the  deflection  is  made  nil  for  both  positions  of  the  rocker; 
that  is, 

Dj  =  Dn  =  0. 
11 


162  ELECTRICAL  MEASUREMENTS 

Then  with  the  first  position  of  the  rocker 

A  =a(r5  +  X)  +  X(r6  +  &). 
B       afo  +  SO  +  Sifa  +  aO 

and  with  the  second  position  of  the  rocker 

A       a'(r6  +  Si)  +  Si(r6  +  X) 
B       a't  +  X 


Equating  these  two  expressions  for  ^  an  equation  results  of  the 

form 

C(X  -  Si)  =  0. 

C  is  a  function  of  the  various  resistances;  all  the  algebraic 
signs  entering  into  it  are  +  so  the  condition  Z)/  =  Dn  —  0 
shows  that 

X  =  Si 

It  will  be  noted  that  this  result-  is  obtained  regardless  of  the 
values  of  A  and  5,  that  is,  without  making  the  galvanometer 
exactly  differential. 

Suppose  DZ  and  DH  are  equal  but  not  zero,  that  is,  that  there 
are  deflections  of  the  same  amount  and  toward  the  same  end  of 
the  scale  for  both  positions  of  the  rocker.  In  the  case  where 
in  =  i'a  and  a  =  a',  that  is,  where  there  is  no  alteration  of  the 
circuit  resistance,  the  relation  between  X  and  S  is  still 

Y          <?    ,rY 

A  =  oi  or  A  = 


N  +  S 

If  the  battery  current  and  a  alter  slightly,  due  to  the  different 
positions  of  the  rocker,  and  the  adjustments  are  made  so  that 
DI  =  I)//,  the  departure  from  the  relation  Si  =  X  is  so  slight 
that  it  may  be  neglected  even  in  precision  work. 

The  Kohlrausch  method  of  employing  the  differential  galva- 
nometer is  the  only  one  adapted  to  work  of  the  highest  precision. 

The  Wheatstone  Bridge. — This  instrument  which  is  so  uni- 
versally used  in  the  determination  of  electrical  resistance 
was  invented  by  Mr.  S.  Hunter  Christie,  of  the  Royal  Military 
Academy  at  Woolwich.  He  published  an  account  of  it  in  the 
Philosophical  Transactions,  under  date  of  Feb.  28,  1833,  calling 


THE  MEASUREMENT  OF  RESISTANCE 


163 


his  invention  "  A  Differential  Arrangement."  The  variable  ratio 
arms  were  added  by  Dr.  Werner  Siemens.  In  1843  Sir  Charles 
Wheatstone  recalled  attention  to  Christie's  device,  giving  him  full 
credit.  At  that  time  Wheatstone  was  one  of  the  leading  scientists 
of  Great  Britain,  and  his  name  became  associated  with  the  instru- 
ment and  has  so  remained. 

Having  the  conductors  arranged  as  in  the  diagram,  Fig.  89, 
the  current  through  the  galvanometer  will  be  zero  only  when 

M      X 

-^  =  j^,  for  to  have  zero  current  in  the  galvanometer,  the  poten- 
tial difference  between  the  galvanometer  terminals  must  be  zero, 
or,  in  other  words,  the  fall  of  potential  along  M  must  be  equal  to 
that  along  X,  and  the  fall  along  N  equal  to  that  along  P. 


M 


FIG.  89. — Diagram  for  Wheatstone  bridge. 

Let  IM,  IN,  Ix,  IP  be  the  unvarying  currents  in  the  respective 
branches;  then  when  IG  =  0,  MIM  =  XIX,  also  NIN  =  PIP, 

MIM  _  XIx 

NIN  ~  P1P 

but  if  no  galvanometer  current  flows, 

IM  =  IN  and  Ix  =  IP 


so 


M 


-~ 


Consequently,  if  three  of  the  resistances  are  known,  the  fourth 


164  ELECTRICAL  MEASUREMENTS 

may  be  determined.  M  and  N  are  called  the  balance  or  ratio 
arms  and  P  the  rheostat  arm  of  the  bridge. 

Auxiliary  Apparatus. — Besides  the  bridge  box,  the  other  neces- 
sary pieces  of  apparatus  are  the  battery  (usually  two  or  three 
cells),  the  keys  KB  and  KG,  the  galvanometer,  shunt,  and  com- 
mutator, see  Fig.  89. 

Keys. — Keys  KB  and  KG  are  usually  combined  to  form  what  is 
called  a  bridge  key,  which  when  depressed  throws  in  first  the 
battery  and  then  the  galvanometer  (to  eliminate  the  effects  of 
inductance  and  capacity).  To  avoid  the  chance  of  leakage  to  the 
galvanometer  and  also  thermo-electric  effects,  care  must  be  taken 
when  manipulating  this  key  not  to  touch  the  metal  work.  The 
commutator  H  is  used  to  reverse  the  battery  current  and  so  to 
eliminate  the  effects  of  thermo-electromotive  forces. 

The  Galvanometer. — The  galvanometer  should  be  one  which  is 
not  affected  by  variations  of  the  local  field  and,  if  possible^  should 
be  critically  damped;  either  a  shielded  Thomson  or  a  D' Arson  val 
instrument  may  be  used. 

In  selecting  a  D' Arson  val  galvanometer  for  bridge  work,  the 
peculiarities  of  the  instrument  should  be  considered ;  for,  suppose 
the  resistance  in  the  bridge  arms  between  the  galvanometer 
terminals  is  low  and  that  the  instrument  is  one,  which,  for  critical 
damping,  requires  that  it  be  in  series  with  a  high  external  resist- 
ance. On  the  passage  of  the  current,  as  soon  as  the  coil  begins 
to  move,  an  e.m.f.  will  be  set  up  in  the  circuit  and  the  motion  will 
be  damped.  Consequently  instead  of  a  sharp,  decided  movement 
of  the  index  the  motion  will  be  so  deliberate  as  to  greatly  increase 
the  difficulty  of  deciding  when  the  bridge  is  in  balance.  Obviously 
it  is  impossible  to  select  a  galvanometer  which  will  be  critically 
damped  for  all  combinations  of  the  bridge  arms,  but  with  care  a 
good  working  compromise  may  be  secured.  In  general,  with  a 
given  sensitivity,  the  shorter  the  period  of  the  instrument,  the 
more  satisfactory  will  its  action  be. 

The  Shunt. — The  shunt,  S,  is  a  bypass  for  the  current  and  is 
placed  between  the  galvanometer  terminals.  It  is  used  during 
preliminary  adjustments  to  protect  the  galvanometer  against 
currents  of  abnormal  strength.  By  means  of  the  movable  arm 
the  value  of  the  shunt  resistance  may  be  altered  so  that  as  the 
adjustment  of  the  bridge  nears  perfection,  a  greater  proportion 


THE  MEASUREMENT  OF  RESISTANCE         165 

of  the  current  can  be  sent  through  the  galvanometer.  During 
the  final  adjustment,  when  full  sensitiveness  is  desired,  the 
movable  arm  should  be  turned  so  far  to  one  side  that  it  breaks 
the  shunt  circuit  and  the  entire  current  flows  through  the 
galvanometer.  The  various  positions  of  the  movable  arm  are 
usually  so  arranged  that  the  fractional  parts  of  the  full  current 
which  can  be  sent  through  the  galvanometer  are  0.001,  0.01,  0.1 
and  1.  When  using  a  Wheatstone  bridge  one  should  always  begin 
measurements  with  the  galvanometer  heavily  shunted.  Violent 
deflections  of  the  instrument  are  thus  avoided. 

The  Null  Method  of  Making  a  Measurement. — The  coil  of 
unknown  resistance  is  inserted,  as  indicated  in  Fig.  90.  All 
connections  must  be  electrically  perfect ;  all  binding  posts 
should  be  screwed  up  tightly,  but  without  using  undue  force; 
all  plugs  should  be  firmly  inserted  and  the  galvanometer  heavily 
shunted.  A  rough  idea  of  the  magnitude  of  X  is  obtained  as 
follows:  Make  M  =  N;  draw  the  1-ohm  plug  in  P;  depress  the 
key  with  care,  being  ready  to  release  it  immediately  should  the 
deflection  of  the  galvanometer  be  violent.  The  deflection  will  be 
assumed  to  be  toward  the  left.  Note  this  deflection,  plug  up  the 
1-ohm  coil,  and  draw  the  5,000-ohm  or  other  high  resistance  plug; 
proceed  as  before.  The  deflection  may  be  toward  the  right; 
it  is  then  known  that  P  and  consequently  X  is  between  1  ohm 
and  5,000  ohms.  If  one  deflection  is  greater  than  the  other, 
it  shows  that  the  proper  value  of  P  is  nearer  the  resistance  which 
gives  the  smaller  deflection.  Next  try  10  ohms  in  P.  Suppose 
the  deflection  to  be  still  toward  the  left;  the  proper  value  of  P 
is  between  10  ohms  and  5,000  ohms.  Proceed  in  this  manner, 
always  narrowing  the  limits  between  which  the  right  value  of 
P  must  be  located.  Having  obtained  an  apparent  balance,  the 
shunt  resistance  is  increased  and  a  better  approximation  obtained. 
Suppose  that  the  bridge  finally  balances  with  P  =  25  +  ohms, 
25  ohms  being  too  small  and  26  ohms  too  large;  then  X  is  between 
25  and  26  ohms.  It  is  obvious  that  the  determination  of  X  is 
good  only  to  about  2  or  3  per  cent.  Suppose  that  X  is  desired 
to  0.1  per  cent.;  then  as  the  smallest  coil  in  P  is  1  ohm,  P  must  be 
between  2,500  and  2,600  ohms  in  order  that  the  smallest  step 
may  represent  most  nearly  the  desired  precision.  Accordingly 


166  ELECTRICAL  MEASUREMENTS 

make  P,  2,500  ohms  and  alter  the  balance  arms  M  and  N  to 
correspond. 

Make  M  =  10  ohms  and  N  =  1,000  ohms;  gradually  increase 
.P  from  2,500  ohms  until  exact  balance  is  obtained,  with  shunt 
removed;  then 

X-      10    P 
"  1,000 

In  the  above  it  has  been  supposed  that  with  M  =  N  the 
deflections  with  P  =  1  ohm  and  P  =  5,000  ohms  were  one  to  the 
right,  the  other  to  the  left.  If  they  had  both  been  to  the  right 
and  the  one  with  P  =  1  ohm  of  the  lesser  magnitude,  then  the 
proper  value  of  P  would  have  been  below  1  ohm  and  X  less  than 
1  ohm.  In  such  a  case  proceed  at  once  to  change  the  ratio  of 
M  and  N  so  that  1  ohm  in  P  balances  0.01  ohm  in  X.  In  other 

M         1 
words,  make  v^  =  j^  and  proceed  as  before  with  the  adjustment 

of  P.  If  P  should  be  greater  than  5,000  ohms,  the  proper  pro- 
cedure may  be  decided  upon  from  the  above  discussion. 

As  a  final  precaution,  all  connections  should  be  gone  over  to 
see  if  they  are  tight  and  all  the  plugs  firmly  in  place;  then  the 
final  balance  should  be  taken.  The  battery  current  should  be 
reversed  and  the  test  repeated;  this  is  necessary  in  order  to  elimi- 
nate thermo-electric  currents.  The  average  result  for  P  is  used 
in  calculating  X. 

The  Deflection  Method. — Referring  again  to  the  example 
just  discussed,  with  M  =  N,  P  was  between  25  and  26  ohms  and  X 
could  be  determined  only  to  2  or  3  per  cent.  Now  suppose  that 
with  P  =  25  ohms,  the  galvanometer  deflects  from  its  zero  posi- 
tion thirteen  divisions  to  the  left,  and  with  P  =  26  ohms  nine 
divisions  to.  the  right;  then  we  may  interpolate,  for  a  change  of 
1  ohm  in  P  causes  the  spot  of  light  to  vary  twenty-two  divisions, 
and  the  proper  value  of  P  for  exact  balance  will  be  25+  ohms 
or  25.59  ohms.  As  the  readings  of  the  deflections  cannot  gener- 
ally be  taken  with  great  accuracy,  25.6  ohms  would  be  the  value 
of  P  to  be  accepted.  It  is  obvious  that  if  this  procedure  be  fol- 
lowed X  may  be  determined  to  %  per  cent,  without  changing 
the  ratio  from  M  =  N.  If  the  ratio  be  changed  the  precision 
may  be  still  further  increased.  This  method  is  used  to  gain 
precision  when  X  is  so  small  that  P  must  be  of  small  value.  This 


THE  MEASUREMENT  OF  RESISTANCE          167 

method  is  slower  in  its  application  than  the  null  method,  and 
the  arms  of  the  bridge  are  more  likely  to  be  overheated.  The 
battery  e.m.f.  must  remain  constant. 

Examples  of  Arrangements  of  Bridge  Tops. — A  very  satis- 
factory form  of  bridge  top  is  shown  in  Fig.  90.  All  the  connec- 
tions made  in  setting  up  the  instrument  are  outside  the  box,  the 
wires  being  attached  to  the  appropriate  binding  posts. 

From  the  plan  of  the  top,  it  will  be  noted  that  there  are  three 
gaps  at  1',  2',  3'  each  marked  Inf;  removing  the  plug  from  any 
one  of  these  gaps  breaks  the  circuit.  The  10,000-ohm  coil  may 
be  used  in  either  the  balance  or  the  rheostat  arm.  Reversal  of 
the  bridge  arms  is  accomplished  by  placing  X  at  3'  instead  of  1', 
the  galvanometer  terminal  being  changed  also.  By  removing 
the  plugs  at  1'  and  2'  and  3',  the  coils  are  divided  into  two  indepen- 
dent sections;  occasionally  this  is  very  convenient  where  the 
box  is  used  for  general  laboratory  purposes. 

Another  design  employing  the  series  arrangement  of  coils  is 
shown  in  Fig.  91.  Here  the  connections  are  permanently  made 
inside  the  box.  The  reversal  of  the  ratio  arms  is  effected  by 
changing  the  plugs  from  positions  1'  to  2'. 

In  Fig.  92  is  shown  a  bridge  employing  the  dial  arrangement 
for  the  rheostat  arm.  The  unknown  resistance  is  inserted  at 
either  1  or  2  according  to  the  ratio  desired.  The  dial  bridge  in 
this  form  is  not  recommended  because  the  condition  of  the  top 
is  not  apparent  at  a -glance  and  there  is  also  difficulty  in  clean- 
ing it. 

A  dial  bridge  with  sliding  in  place  of  plug  contacts  in  its 
rheostat  arm  is  shown  in  Fig.  93. 

In  this  bridge  the  ratio  coils  are  arranged  as  suggested  by 
A.  Schone3  (see  Fig.  94).  There  are  two  coils  of  each  of  the 
following  denominations,  1,  10,  100,  1,000  ohms.  All  the  coils 
have  one  terminal  attached  to  the  central  copper  bar  which  is 
inside  the  box,  the  other  terminals  being  connected  to  the  plug 
blocks.  Two  plugs  are  ordinarily  used.  When  inserted  as 

shown,  -^  =  -JJT-.     The  advantages  of  this  arrangement  are  the 

ease  with  which  the  arms  may  be  reversed,  the  reduction  in  the 
number  of  plug  contacts,  and  the  possibility  of  obtaining  the 
the  same  ratio  by  using  different  coils  of  the  same  denomination, 

thus  giving  a  check  on  the  value  of   ,,-. 


168 


ELECTRICAL  MEASUREMENTS 


M 


-N 


A    GKfl     O 


oft     Oiooff     Otoofl 


O 

Therm. 


FIG.  90. — Wheatstone  bridge  top  with  plug  connections. 


^0.10.20.30.4. IP, j 13 :         4 _1( )20 

S^iOOOOOOOOO 


1000     100      10        1 


00   4000  3000  2000  1000  400   300 


FIG.  91. — Wheatstone  bridge  with  internal  connections  and  reversible 

ratio  arms. 


THE  MEASUREMENT  OF  RESISTANCE 


169 


For  field  work,  portable  bridges  are  used.  One  design  is 
shown  in  Fig.  95.  The  carrying  case  contains  the  bridge  pro- 
per, the  galvanometer,  which  is  of  the  D'Arsonval  type,  and  a 


FIG.  92. — Wheatstone  bridge  with  dial  arrangement  of  rheostat  coils. 


FIG.  93. — Wheatstone  bridge  with  Schpne  ratio  coils  and  sliding-dial 
rheostat  coils. 

few  cells  of  dry  battery.     In  the  example  here  shown  the  decade 
arrangement  with  sliding  contacts  is  adopted. 


170 


ELECTRICAL  MEASUREMENTS 


Calibration  of  a  Resistance  Box. — In  order  that  any  changes 
in  the  coils  may  be  detected,  all  resistance  boxes  and  Wheat- 
stone  bridges  should  be  calibrated  occasionally.  A  convenient 


FIG.  94. — Schone  arrangement  of  ratio  coils  for  Wheatstone  bridge. 


M  LKDSSNORTHRUP  DIAL  DECADE  JESTING 
TYPE  S       jrssrtr 


THE  LEEDS  &NORTHRUP  CO. 

PHILADELPHIA. 


FIG.  95. — Portable  Wheatstone  bridge  with  sliding-dial  coils. 

method  of  doing  this  with  sufficient  accuracy  for  general  labora- 
tory work,  and  one  for  which  the  apparatus  is  readily  assembled, 
is  shown  in  Fig.  96.  It  is  a  substitution  method  involving  the 
use  of  the  bridge  principle. 


THE  MEASUREMENT  OF  RESISTANCE 


171 


Definiteness  is  the  only  requirement  in  the  balancing  re- 
sistances. They  must  not  change  through  heating  or  be  erratic 
through  ill-fitting  plugs  or  defective  sliding  contacts. 

The  box  to  be  calibrated  is  placed  in  series  with  the  standard 
as  shown.  If  the  resistances  of  the  equal  extension  coils,  m, 
are  properly  adjusted  to  that  of  the  slide  wire,  a  given  dis- 
placement of  the  slider  may  be  made  to  correspond  to  an  assigned 
percentage  difference  of  X  and  S. 

Suppose  the  slide  wire  has  a  length  of  1  meter  and  a  resistance 
of  10  ohms.  It  is  desired  that  a  difference  of  Jfo  per  cent, 
between  X  and  S  shall  correspond  to  a  displacement  of  the 
balance  point  of  10  cm.  When  X  =  S,  the  balance  point  is  to 
be  at  the  middle  of  the  slide  wire. 


i 

FIG.  96. — Connections  for  comparing  resistance  boxes. 


A  displacement  of  10  cm.  to  the  left  takes  1  ohm  from  the  left- 
hand  side  of  the  bridge  and  adds  it  to  the  right-hand  side.     Then 


m 


and  ™  " 


LOO         r 

Assume  a  balance  to  be  obtained  with  the  1-ohm  coil  in  X 
by  unplugging  the  corresponding  coil  in  the  balancing  resistance, 
the  standard  S  having  been  cut  out.  If  needful,  R  may  be  used 
to  bring  the  balance  point  to  the  middle  of  the  slide  wire.  The 
reading  of  the  slider  is  taken  and  then  the  standard  S  is  sub- 
stituted for  X.  If  X  =  S  there  will  be  no  change  in  the  balance 
point;  if  X  differs  from  S,  balance  is  restored  by  moving  the  slider 
and  another  reading  taken.  The  difference  of  the  two  readings 
and  the  known  displacement  of  the  slider  corresponding  to  Y\§ 


172 


ELECTRICAL  'MEASUREMENTS 


per  cent,  allows  the  percentage  difference  of  the  two  coils  to  be 
calculated  nearly  enough  for  practical  purposes.  The  1-ohm  coil 
is  thus  compared  with  the  standard  ohm,  then  the  2-ohm  coil 
with  the  sum  of  the  1-ohm  and  the  standard,  then  the  second 
2-ohm  coil  with  the  first  and  so  on. 

The  10-ohm  coil  may  be  compared  with  a  10-ohm  standard  and 
the  values  of  the  20-ohm,  50-ohm,  100-ohm  and  other  coils 
determined  by  comparison  with  those  previously  calibrated,  or 
the  whole  series  may  be  built  up  from  the  standard  ohm. 

After  one  box  has  been  calibrated,  others  may  readily  be  com- 
pared with  it  by  this  method. 


FIG.  97.- 


-Arrangement  for  compensating  large  thermo-electromotive 
forces. 


Compensation  for  Large  Thermo-e.m.f. — Occasionally  in 
special  bridge  arrangements  the  unavoidable  inequalities  of 
temperature  in  the  apparatus  may  cause  thermo-e.m.fs.  of 
sufficient  magnitude  to  drive  the  galvanometer  spot  off  the 
scale.  In  many  cases  such  e.m.fs.  may  be  compensated,  if 
they  are  reasonably  constant  and  the  galvanometer  can  be  used 
on  closed  circuit. 

Referring  to  Fig.  97,  R  is  a  high  resistance  of  several  thousand 
ohms,  S.W.  a  slide  wire;  by  adjusting  the  slider,  the  galvanometer 
may  be  brought  to  zero;  then  the  bridge  is  balanced  as  usual. 

Slide-wire  or  Divided-meter  Bridge. — In  this  simple  form 
of  Wheatstone  bridge,  shown  in  Fig.  98,  two  of  the  arms  are  re- 
placed by  the  two  sections  of  a  uniform  wire. 

In  the  diagram  the  heavy  lines  represent  copper  strips  of  low 
resistance  with  gaps  at  a,  6,  c,  d.  On  each  side  of  each  gap  is  a 


THE  MEASUREMENT  OF  RESISTANCE         173 

binding  post  so  that  the  gap  may  be  closed  by  a  strap  of  low  re- 
sistance or  by  a  resistance  coil,  as  is  desired.  Between  e  and  /  is 
stretched  a  wire  of  high  resistance.  It  is  about  a  millimeter  in 
diameter  and,  in  this  form  of  bridge,  intended  to  be  just  1  meter 
long.  A  slider,  s,  makes  contact  at  any  desired  point  along  the 
wire  and  its  position  may  be  read  off  on  a  scale  divided  into  milli- 
meters. It  is  intended  that  e  and  the  zero  of  the  scale  shall  be 
coincident.  The  connections  of  battery  and  galvanometer  are 
generally  as  shown,  and  this  is  usually  the  more  sensitive  arrange- 
ment. If  the  battery  and  galvanometer  are  interchanged,  the 
resulting  arrangement  will  be  less  disturbed  by  thermal  e.m.fs. 
at  the  contact  s. 

To  make  a  measurement,  the  simplest  process  would  be  to  close 
the  gaps  at  a  and  b  by  straps,  place  at  d  the  unknown  resistance 


FIG.  98. — Diagram  for  slide-wire  bridge. 

X,  and  at  c  the  known  resistance  S,  the  best  value  of  which  would 
be  about  the  same  as  X.  The  slider  s  would  then  be  pressed 
carefully  down  upon  the  wire  at  one  point  after  another  until 
one  was  found  where  the  galvanometer  remained  undeflected, 
i.e.,  where  opening  and  closing  at  s  did  not  cause  motion  of  the 
galvanometer  index.  Let  I  represent  the  scale  reading  in  milli- 
meters, i.e.,  I  =  distance  e's.  As  e'f  =  1,000  mm.,s/  =  1,000  —  I. 

Then,  by  the  bridge  principle,  X  =  S  -      ~f~r'      But    the    wire 

res.  01  L 

is  assumed  to  be  of  uniform  resistance  per  unit  length,  so 
that  the  resistances  of  the  two  parts  of  the  wire  are  pro- 
portional to  their  lengths.  Hence,  if  the  resistances  of  the 
leads  from  e'  to  c  and  from  f  to  d  are  assumed  to  be  zero, 

(1,000  -  I). 
X  =S        — 

Resistances  at  Ends  of  Bridge. — The  leads  at  the  ends  of  the 
bridge  may  not  be  of  negligible  resistance,  and  there  may  be 


174  ELECTRICAL  MEASUREMENTS 

- 

an  inaccuracy  in  placing  the  zero  of  the  scale  opposite  the  end 
of  the  slide  wire.  The  resistances  between  e'  and  the  battery 
terminal  h,  and  between  /  and  the  battery  terminal  i  act  as 
prolongations  of  the  corresponding  ends  of  the  slide  wire.  Let 
n\  denote  the  number  of  millimeters  of  the  wire  which  would 
have  the  same  resistance  as  e'h,  and  n2  the  corresponding 
number  for  fi.  Then  if  n\  and  n2  were  known,  their  effect 
would  be  allowed  for  by  writing 

a  1,000  -l  +  n2 
7 — T 

X 

The  values  of  HI  and  n2  may  be  determined  as  follows : 
After  thoroughly  cleaning  the  surfaces  of  contact  insert  the 
straps  at  a  and  b.     Place  at  c  a  coil  of  A  ohms  and  at  d  a  coil  of 
B  ohms.     A  and  B  must  be  different.     Call  the  reading  of  the 
slider  when  the  balance  has  been  obtained  L.     Then 


B       1,000  -  h  +  n2 

Interchange  A  and  B  and  obtain  a  new  balance  at  12. 
Then 

D  7         i      „ 

D  12      \     ill 

A  =  1,000  -  12  +  n2 
A  li+ni 


A  +  B      1,000 
B  L 


A  +  B      1,000 

Bh  -  A12 


A-B 

Similarly 

£(1,000  -12)  -A  (1,000  - 


Extension  Coils.  —  If,  in  measuring  X,  the  balance  point  falls 
near  one  end  of  the  bridge,  the  shorter  section  of  the  wire  cannot 
be  determined  with  accuracy.  Again,  if  equal  coils  are  being 
compared,  greater  accuracy  in  setting  s  may  be  desired.  In 
either  case,  it  would  be  advantageous  to  use  a  longer  wire.  As 
this  would  be  inconvenient,  the  same  result  is  attained  by  insert- 


THE  MEASUREMENT  OF  RESISTANCE          175 

ing  resistance  coils  at  the  gaps  a  and  b.  The  effect  of  these,  so 
far  as  the  balance  is  concerned,  is  the  same  as  if  the  wire  had  been 
extended  on  each  side  by  the  addition  of  such  a  length  as  would 
have  the  same  resistance  as  the  coils.  Therefore,  the  equivalent 
lengths  of  these  coils  in  millimeters  of  the  slide  wire  must  be 
determined.  Let  mi  denote  this  quantity  for  the  coil  at  a  and 
m2  that  for  the  coil  at  b.  Then  when  measuring  X, 

g  1,000  -  l  +  n,  +  m2 

.A  —  o  7 .  , • 

l  +  ni  +  mi 

The  values  of  mi  and  m2  may  be  determined  as  follows :  place  at 
c  a  resistance  of  E  ohms  and  at  d  another  known  resistance  of  B 
ohms.  Close  both  a  and  b  by  the  straps  and  balance  the  bridge. 
Call  the  reading  li.  Then 

E  h  +  ni 

B       1,000  -  h  +  n* 

Now  insert  at  a  the  coil,  the  equivalent  length  of  which  is  desired, 
and  obtain  a  new  balance.  Call  the  reading  12.  Then 

E  _     Z2  -f  fti  +  mi 
B  =  1,000  -1T+W2 

.*.  mi  =  (it  -  y  (I  + 1 

and  similarly  for  m2. 

In  using  equal  extension  coils,  it  is  necessary  to  have  the 
known  resistance  S  (at  c)  so  nearly  equal  to  X  that  the  balance 
point  will  come  upon  the  slide  wire.  If  the  extension  coils  are 
unequal,  then  the  ratio  of  S  to  X  must  be  such  as  to  accomplish 
this;  or  if  S  is  of  a  fixed  value,  then  the  ratio  of  mt  to  m2  must  be 
properly  adjusted.  If  S,  mi  and  m2  are  all  fixed,  the  range 
of  the  apparatus  is  limited. 

With  a  more  elaborate  construction,  and  when  used  with  due 
precautions  to  eliminate  thermo-currents,  contact  resistances, 
etc.,  the  slide  wire  bridge  becomes  useful  in  work  of  the  highest 
precision. 

Carey  Foster  Method  for  Comparing  Two  Nearly  Equal 
Coils. — This  method  is  primarily  designed  for  the  comparison  of 
nearly  equal  resistances;  it  therefore  lends  itself  readily  to  the 
determination  of  temperature  coefficients  and  to  the  verification 
of  standard  coils. 


176  ELECTRICAL  MEASUREMENTS 

The  coils  to  be  compared  are  inserted  at  a  and  b  (Fig.  98). 
Let  their  resistances  be  A  and  B;  two  approximately  equal  re- 
sistances S  and  S'  are  inserted  at  c  and  d]  this  insures  that  the 
balance  point  will  fall  near  the  middle  of  the  slide  wire.  Let  R 
be  the  resistance  per  unit  length  of  the  slide  wire,  L  the  total 
length  of  slide  wire  in  divisions,  l\  and  1%  the  readings  of  the  slider 
at  balance.  Then 

S_  A 

S'  ~  B  +  n 


If  A  and  B  are  interchanged, 

S  B  +  mR  + 


So 
and 


S'  ' '  A  +  nzR  +  (L  -  h)R 
S  A  +  mR  +  hR 


S  +  8'       A  +  B  +  niR  +  n2R  +  LR 
S  B  +  niR  +  12R 


S  +  S'  ~  A  +  J5  +  mR  +  nzR  +  LR 
.'.  A  -  B  =  R(12  -  h)  =  RD 


D  is  the  difference  of  the  two  readings  of  the  slider. 

The  difference  of  the  resistances  of  the  coils  is  seen  to  be 
equal  to  the  resistance  of  the  portion  of  the  slide  wire  between 
the  two  balance  points.  It  is  to  be  noticed  that  this  result  is 
independent  of  S  and  Sf  and  of  n\  and  n^  as  well  as  of  con- 
tact resistances,  if  these  factors  remain  constant  during  the  test. 
Some  convenient  device  must  be  adopted  for  interchanging  the 
coils  without  removing  them  from  their  cooling  baths  and  with- 
out handling,  and  as  it  is  the  difference  of  two  nearly  equal 
quantities  which  is  involved,  extraneous  resistances  due  to  change 
of  connections  and  contacts  must  be  carefully  avoided.  Fig.  99 
shows  a  form  of  bridge  especially  designed  for  carrying  out  the 
Carey  Foster  test. 

The  interchange  of  the  coils  is  effected  by  raising  the  contact 
switch  K,  turning  it  through  one-half  a  revolution  and  then 
lowering  it. 

To  adapt  the  device  to  the  comparison  of  high  as  well  as  low 
resistances,  several  pairs  of  coils  (SS')  must  be  provided  in  order 
that  a  sensitive  bridge  arrangement  may  be  maintained.  A 
number  of  slide  wires  of  different  resistance  per  unit  length, 


THE  MEASUREMENT  OF  RESISTANCE 


177 


together  with  means  for  readily  inserting  them  in  the  circuit, 
are  also  required.  Three  such  wires  are  provided,  any  one  of 
which  may  be  used  at  will,  and  to  obtain  the  effect  of  a  wire  of 
very  low  resistance,  the  slide  wire  proper  may  be  shunted. 
This  is  effected  by  the  link  seen  at  the  front  of  the  switchboard. 


FIG.  99. — Carey  Foster  bridge." 

Determination  of  the  Resistance  per  Unit  Length  of  the  Slide 
Wire. — To  determine  R,  the  resistance  per  unit  length  of  the  slide 
wire,  the  process  of  measurement  may  be  inverted.  Let  A  and 
B  be  two  coils  of  nearly  equal  resistance,  so  that  the  balance 

points  will  fall  near  the  middle  of  the  bridge;  only  one  of  the  coils 

12 


178  ELECTRICAL  MEASUREMENTS 

need  be  known  with  exactness.     A  balance  is  effected  in  the  usual 
way.     Then  by  the  law  of  the  bridge, 

A  -  B  =  RDi. 

The  known  coil  is  then  shunted  by  a  resistance  C  which  is  of 
such  a  value  that  the  balance  points  fall  near  the  ends  of  the  slide 
wire.  This  shunted  coil  is  then  compared  with  the  coil  A  which 
gives 

RC 
A   -  -gq^ 

therefore 


When  comparing  coils  of  moderate  resistance  it  may  happen 
that  their  difference  is  so  great  that  the  slide  wire  is  not  of 
sufficient  length;  in  such  a  case  the  larger  resistance  may  be 
shunted,  a  comparison  effected  in  the  usual  way  and  the  shunt 
allowed  for.  The  accuracy  with  which  the  shunt  must  be  known 
depends  on  its  ratio  to  the  resistance  of  the  coil  around  which  it  is 
placed. 

Calibration  of  a  Slide  Wire.  —  In  dealing  with  the  slide-wire 
bridge,  it  has  been  assumed  that  the  wire  is  of  uniform  resistance 
per  unit  length.  In  order  that  troublesome  corrections  may  be 
avoided  every  effort  should  be  made  to  have  this  assumption 
strictly  true.  If  a  case  arises  where  the  wire  must  be  tested  for 
uniformity,  it  may  be  divided  into  sections  of  equal  resistance  by 
one  of  several  different  methods.  If  the  wire  be  uniform  these 
sections  will  be  of  equal  length;  if  they  differ  in  length,  corrections 
may  be  determined  by  which  a  reading  on  the  wire  may  be 
reduced  to  the  value  it  would  have  had  if  the  wire  had  been  of 
uniform  resistance  per  unit  length. 

Carey  Foster  Method  of  Calibrating  a  Slide  Wire.  —  Referring 
to  the  demonstration  for  the  Carey  Foster  method  of  comparing 
two  coils  (page  176),  it  is  seen  that  their  difference  is  independent 
of  S  and  $';  the  relative  values  of  S  and  S',  however,  determine 
the  position  of  the  balance  points  on  the  slide  wire.  Let  A  and 
B  be  two  nearly  equal  resistances  one  of  which  is  shunted  by  a 
resistance,  C,  so  that  Z2  —  Zi  has  the  desired  value.  The  two 
sections  [of  a  second  slide  wire  replace  the  coils  S  and  Sf  ordi- 


THE  MEASUREMENT  OF  RESISTANCE 


179 


narily  used  at  the  gaps  c  and  d.     The  connections  are  then  as 
shown  in  Fig.  100. 

The  contact  q  is  placed  at  the  zero  of  the  slide  wire  and  the 
contact  0  adjusted  until  balance  is  obtained.  The  coils  are  then 
interchanged  and  the  slider,  q,  is  adjusted.  Then 

J3C* 

A  —  -5- — ~  =  resistance  of  section  12  —  0 

£>  -f-  C 

The  coils  are  returned  to  their 
original  position,  q  remaining 
fixed,  and  the  contact  0  ad- 
justed until  the  balance  is 
again  attained.  The  coils  are 
then  interchanged  and  the  bal- 
ance obtained  again  by  moving 
the  contact  q.  The  slide  wire 
is  thus  divided  into  sections 
each  having  a  resistance, 

A  -  r 


S      I              S' 

1  

0 

i-  r 

1 

UJ3_ 

Jc"-       ^d'  '£ 

FIG.  100.- 
method  f 

"Q 

-Diagram  for  Carey 
or  calibrating  a  slide 

Foste 
wire. 

BC 


B  +  C 

As  this  difference  must  remain  constant,   the  coils  employed 

should  be  of  manganin. 
Barus  and  Strouhal  Method  for  Calibrating  a  Slide  Wire. — 

This  method  is  a  simple  application  of  the  projection  of  poten- 
tials; the  wire  to  be  calibrated 
is  placed  in  parallel  with  a 
series  of  movable  coils  having 
nearly  equal  resistances.  For 
convenience  they  may  be 
ranged  along  a  board  parallel 
to  the  slide  wire  with  their 

FIG.  101. — Diagram  for  Barus  and    terminals   dipping   into  mer- 
Strouhal    method    for     calibrating    a 
slide  wire. 

One  of  the  coils,  a,  is  selected 

as  a  standard,  the  galvanometer  attached  to  one  terminal  of 
it  and  balance  obtained  by  use  of  the  slider.  The  galvanometer 
wire  is  then  transferred  to  the  other  terminal  of  the  coil  and  a 
second  balance  obtained  by  use  of  the  slider.  Coil  a  is  now  in- 
terchanged with  coil  b  and  the  operation  repeated.  Thus,  by 


180 


ELECTRICAL  MEASUREMENTS 


successively  interchanging  the  coils  with  a  and  finding  the  cor- 
responding balance  points,  a  series  of  length  having  equal  resist- 
ances may  be  set  off  on  the  slide  wire. 

Thomson  Bridge  Method  for  Calibrating  a  Slide  Wire.— 
Connections  are  made  according  to  Fig.  102.  CD  is  a  resistance 
which  determines  that  of  the  steps  into  which  the  slide  wire  is  to 
be  divided.  It  is  connected  in  series  with  the  slide  wire  by  a 
resistance  R  which  is  considerably  greater  than  that  of  the  wire 
and  which  can  be  short-circuited.  The  coils  M,  N,  m,  n,  should 


£  1£11    ,1  v,.       M       m 

fulfill   the  condition  -^  =  — 

N       n 


If  this  condition  is  exactly  ful- 


M  N 


filled,  the  settings  will  be  independent  of  the  resistance  between 
D  and  l\]  to  make  sure  that  this  is  so  l\  is  set  at  any  point  on  the 

slide  wire,  R  is  short-circuited 
and  a  balance  obtained  by 
adjusting  12  The  short-cir- 
cuit around  R  is  then  re- 
moved. The  balance  should 
remain  undisturbed  and  this 
should  be  true  whatever,  the 
setting  of  li.  A  more  severe 

FIG.    102.  —  Diagram  for   Thomson-    test  is  to  have  a  break  at  R, 
bridge  method  for  calibrating  a  sli,       ^  ^  tQ  makg  R  =   ^       Jf 

this    test  is  satisfactory,  the 

slider  li  may  be  set  at  various  points  along  the  wire  and  bal- 
ances   obtained  by  moving  Z2.     The  resistance  of  the  sections 

will  then  be  r/2  -  zi  =  rCD  l-- 


Calibration  Corrections.  —  If  it  appears  from  the  data  obtained 
by  any  of  these  methods  that  the  wire  is  not  uniform,  it  is  best 
to  replace  it  by  another.  If  circumstances  preclude  this,  the 
calibration  observations  may  be  reduced  as  follows: 

It  is  desired  to  find  the  corrected  values  of  the  readings  to  be 
inserted  in  the  formulae  already  given  for  the  slide-wire  bridge; 
that  is,  the  readings  on  a  uniform  wire  of  the  same  total  resistance 
as  the  wire  actually  used. 

The  lengths  of  the  sections  of  equal  resistance  are  plotted 
as  ordinates.  The  positions  of  the  lower  ends  of  the  sections 
are  taken  as  abscissae.  A  smooth  curve  is  then  drawn  through 


THE  MEASUREMENT  OF  RESISTANCE 


181 


the  points.  This  curve  shows  what  the  length  of  the  section 
would  be  if  its  lower  end  were  at  any  point  on  the  slide  wire. 

Call  the  ordinate  at  x  =  0,  y\.  If  the  lower  end  of  the  section 
were  at  0  the  upper  end  would  be  at  x  =  y^.  Look  up  the 
ordinate  at  that  point,  call  it  yZj  add  it  to  yi  and  determine  ys 
and  so  on.  Let  y\  +  y2  .  .  .  +  yn  =  S. 

The  resistances  of  the  section  S}  denoted  by  Ra,  and  of  the 
whole  wire  between  0  and  100,  denoted  by  RWo,  are  then  measured 
by  any  convenient  method.  Obviously,  the  section  S  is  made 

Ra 

up  of  n  smaller  sections  each  having  a  resistance  — • 


FIG.  103.  —  Pertaining  to  calibration  of  slide  wire. 


The  resistance  of  the  section 


7?  27? 

is  -—  ,  of  section  y\  +  y^  -    *' 


of  section 
nR8 


O  D 

2/2  +  2/a,    ~~;  of  section  yl  + 


2/3 


n 


These  resistances  may  be  plotted  as  ordinates,  using  as 

abscissae  the  values,  yl}  yi  +  yz,  yi  +  y2  +  ys,  etc.  (Fig.  103). 
At  the  100  mark  #100  is  laid  off;  a  straight  line  drawn  through 
this  point  and  the  scale  reading  0  is  the  line  along  which  the 
points  previously  plotted  would  lie  if  the  wire  were  uniform. 

Take  any  scale  reading,  l\  the   resistance  of  the  length  I  is 
RI.     The  corresponding  reading  on  the  uniform  wire  is  obtained 


182  ELECTRICAL  MEASUREMENTS 

by  projecting  this  resistance  upon  the  straight  line  as  indicated, 
giving  lc  as  the  corrected  value  of  the  reading. 

Instead  of  actually  making  the  plot,  the  corrections  are 
better  determined  as  follows. 

Assuming  the  wire  to  be  a  meter  long,  the  resistance  per  cm. 

of  the  uniform  wire  would  be  T^TT' 

1UU 

Let  (yi)c  be  the  corrected  value  of  y\. 

(yl  -f  yz)c  be  the  corrected  value  of  (yi  +  yz). 

(2/1+2/2+  .  •  .  +2/n)c  be  the  corrected  value  of  (2/1+2/2+  .  .  .  +yn). 
Then 

/       s      -RlOO  Rs 


v    RWQ       nRs 

+   2/2   +     .   .   -  +   Vnh 


The  corrections  are 

_    /        \ 

Cl  • 


These  corrections  may  be  plotted  using  scale  readings  as 
abscissae. 

General  Discussion  of  the  Wheatstone  Bridge. — In  order  to 
set  up  and  use  a  Wheatstone  bridge  to  the  best  advantage,  certain 


THE  MEASUREMENT  OF  RESISTANCE 


183 


points  brought  out  by  a  study  of  the  theory  of  the  instrument 
must  receive  attention. 

Galvanometer  Current. — The  general  expression  for  the  current 
through  the  galvanometer  in  terms  of  the  resistances  of  the  vari- 
ous bridge  arms  and  the  electromotive  force  and  resistance  of 
the  battery  is  readily  deduced.  However,  a  simpler  and  more 
useful  formula  is  that  connecting  the  total  bridge  current  with 
the  current  through  the  galvanometer,  for  in  many  cases  the 
bridge  current  is  regulated  by  a  rheostat  rather  than  controlled 
solely  by  the  e.m.f .  of  the  battery  and  by  the  various  resistances. 

Suppose  the  connections  to  be  those  given  in  Fig.  104A,  and 
assume,  following  Maxwell,  that  the  meshes  are  traversed  by 
currents  (x  +  y),  x  and  IB  as  shown  in  the  figure,  also  that  the 


FIG.  104. — Mesh  diagrams  for  Wheatstone  bridge. 

resistances  of  the  various  branches  are  M,  N,  X,  P,  RG  and 
B  and  that  the  electromotive  force  of  the  battery  is  E.  By 
KirchofFs  corollaries 

(x  +  y)  (M  +  RG  +  X)  -  xRG  -  IBX  =  0 
(x)  (N  +P  +  RG)  -  (x  +  y)  RG  -  IBP  =  0. 

Solving  for  y,  which  is  the  true  galvanometer  current,  gives 

IBl(NX  -  MP) 
IG>       RG(M  +  N  +  X  +  P)  +  (N  +  P)(M  +  X) 

The  important  case  is  when  the  bridge  is  nearly  balanced.  Then 
if  B  is  the  total  resistance  in  the  battery  circuit  outside  of  the 
bridge, 

E 

— pv-  nearly  enough. 


" 


"M 


X+P 


184  ELECTRICAL  MEASUREMENTS 

If  the  connections  are  as  shown  in  Fig.  1045, 

T  lB^MP  ~  NX^ 

IG*      RG(M  +  N  +  X+P)  +  (M 

and 


" 


M 


By  use  of  these  equations  it  is  easy  to  determine  whether 
or  not  any  galvanometer  will  give  results  of  the  desired  pre- 
cision, for  the  maker  will  furnish  a  statement  of  the  sensitivity 
of  the  instrument  —  that  is,  the  deflection  per  unit  current  at  a 
scale  distance  of  1  meter,  the  galvanometer  being  in  proper 
adjustment. 

The  Best  Resistance  for  a  Thomson  Galvanometer  When 
Used  with  a  Wheatstone  Bridge.  —  In  general  terms,  the  gal- 
vanometer should  have  a  high  or  a  low  resistance  depending  on 
whether  high  or  low  resistances  are  to  be  measured.  The 
magnitudes  of  the  bridge  arms  being  fixed,  the  galvanometer 
having  the  best  resistance  is  that  one  which  will  give  the  great- 
est deflection  when  the  arm  P  is  changed  from  the  condition  of 
perfect  balance  by  a  given  amount.  It  has  previously  been 
shown  that  if  the  coils  of  a  Thomson  galvanometer  are  always 
wound  on  the  same  bobbin,  the  galvanometer  constant  is  given 
by  G  =  K\/RG,  the  effect  of  the  insulation  being  neglected; 
consequently,  if  the  time  of  vibration  is  kept  constant,  the 
deflection  may  be  represented  by 

D  =  KleVRe  (3) 

K  is  seen  to  be  the  deflection  per  ampere  for  an  instrument  having 
a  resistance  of  1  ohm.     Using    (1) 


D    -  KI  V/T  -  ,      KI*(NX  a  ,    .. 

u«v*°      Ra(M  +  N  + 


This  is  to  be  made  a  maximum,  RG  being  the  only  variable. 
It  will  be  found  that 

dD  _(M±jQ_(^  +  P) 

'          KQ  ~  '    M+N+X+P 


Inspection  shows  that  this  result  corresponds  to  a  maximum 


THE  MEASUREMENT  OF  RESISTANCE 


185 


value.  Therefore,  the  galvanometer  should  have  a  resistance 
equal  to  the  parallel  resistance  of  the  bridge  arms  between  its 
terminals. 

The  effect  of  a  departure  from  this  best  value  of  the  galvanome- 
ter resistance  may  be  seen  from  the  following:  Let  the  actual 
resistance  of  the  galvanometer  be  n  times  that  of  the  ideal 
instrument;  that  is,  let 

f~\/T      I       VWA7"      I       D\ 

(5) 


R° 


n 


M+N+X+P 


1.2 1 


0.8 


Ordinates 


Deflection,  Obtained 


Max  Obtainable  Den. 


n+l 


8 


16 


20 


24 


FIG.  105. — Showing  effect  of  change  of  galvanometer  resistance  on  the 
sensitivity  of  a  Wheatstone  bridge  when  a  Thomson  galvanometer  is 
used. 

Substitution  of  the  value  of  RG  in  (3A)  gives  as  the  corresponding 
value  of  the  deflection, 

KIBl(NX  -  MP)  Vn 

"  (n  +  1)  V(M  ~+X)(N  +  P)  (M  +  N  +  X  +  P) 
The  maximum  deflection  will  be  attained  when  n  =  1.     Con- 
sequently the  ratio  of  the  actual  to  the  maximum  possible  de- 
flection of  the  galvanometer  is 


D 

Dmax 


(6) 


The  values  of  this  ratio  are  plotted  in  Fig.  105. 

Best  Position  for  the  Galvanometer.  —  If  the  galvanometer 
be  of  fixed  resistance  and  if  a  definite  e.m.f.  be  impressed  at 
the  bridge  terminals  the  magnitude  of  the  galvanometer  current 
may  be  considerably  influenced  by  the  relative  positions  of  the 
galvanometer  and  battery. 


186  ELECTRICAL  MEASUREMENTS 

• 

For  suppose  the  actual  value  of  P  differs  from  that  necessary 
for  a  perfect  balance  by  an  amount  5P,  then  referring  to  equations 
(1)  and  (2)  and  substituting  the  approximate  values  of  IB, 

-EM5P 

" 


-EMdP 


~  Denom.i 
and 

EMdP  _ 

"  R 


M+N+X+P 

EMdP 
~  Denom.2 

The  better  arrangement  will  be  the  one  corresponding  to 
the  equation  having  the  smaller  denominator. 

Denom.i-  Denom.2  =  £G[(M  +  AO(X  +  P)-  (M  +  X)(N  +  P)]  ' 

=  RG[(M  -  P)(X  -  N)]  (7) 

From  this  it  is  seen  that  if  the  opposite  resistances  are  equal, 
the  sensitiveness  is  the  same  for  both  arrangements.  If  the 
algebraic  sign  of  the  bracket  is  +  ,  Denom.2  is  less  than  Denom.i 
and  the  second  connection  should  be  used;  if  it  be  —  ,  the  first 
is  to  be  employed. 

The  better  arrangement  is  the  one  where  the  galvanometer 
joins  the  junction  of  the  two  highest  resistance  bridge  arms  to 
the  junction  of  the  two  lowest.  An  exact  discussion  of  the 
more  complete  formula  which  includes  the  e.m.f  .  and  the  resist- 
ance of  the  battery  gives 

Denom.!  -  Denom.2  =  (RG  -  B)(M  -  P)(X  -  N).      (8) 

Considering  the  battery  and  the  galvanometer,  the  one  having 
the  higher  resistance  should  join  the  junction  of  the  two  highest 
to  the  junction  of  the  two  lowest  bridge  arms.  The  importance 
of  the  proper  relative  position  of  the  battery  and  galvanometer 
increases  with  the  disparity  of  the  bridge  arms. 

As  an  illustration,  consider  the  bridge  shown  in  Fig.  106  where 
there   is   a   great   difference   in   the   bridge   arms.     Denom.i  - 
Denom.2  is  +  ,  so  the  second  connection  should  be  used. 


THE  MEASUREMENT  OF  RESISTANCE 


187 


The  second  arrangement  is  about  23  times  as  sensitive  as  the 
first.  However,  as  the  total  bridge  current  is  about  44  times  as 
great,  the  possibility  of  overheating  a  low-resistance  arm  of  the 
bridge  should  be  kept  in  mind.  This  is  seen  from  the  following, 
where  E'  has  been  assumed  as  2  volts. 

Watts  dissipated  in  the  bridge  arms, 

M  N  x  P 

With  the  first  connection 0 . 000004     0 .  Q04       0 . 00004      0 . 04 

With  the  second  connection. ...     0.9  0 . 0009     0 . 09  0 . 00009 

In  the  second  case  there  is  a  possibility  that  the  arm  M  may 
be  overheated  if  the  current  be  kept  on  continuously. 


Approx. 


E'dP 


E'SP 
440,000 


*G   ~   10,200,000 

FIG.  106. — Showing  effect  of  relative  positions  of  battery  and  galvanometer 
on  the  sensitiveness  of  a  Wheatstone  bridge. 

Sensitiveness  Attainable  with  the  Wheatstone  Bridge. — The 

sensitiveness  of  a  bridge  arrangement  may  always  be  increased 
by  increasing  the  bridge  current.  The  limit  to  this  increase  is 
fixed  by  the  carrying  capacity  of  the  bridge  arm  which  will 
safely  stand  the  least  current.4 

With  coils  of  like  construction  but  of  different  resistances 
the  allowable  energy  losses  are  the  same,  that  is, 

(I')ZR  =  k    or    I'\/R  =  Vk,  a  constant.  (9) 

/'  is  the  allowable  current  and  k  the  allowable  heating  loss  in 
watts;  k  depends  upon  the  construction  and  manner  of  using  the 
coils. 

In  planning  new  work  it  is  frequently  of  importance  to  calculate 


188  ELECTRICAL  MEASUREMENTS 

the  deflection  which  would  be  obtained  if  some  particular  gal- 
vanometer were  used. 

Suppose  that  the  maximum  allowable  bridge  current,  I'B,  is 
fixed  by  the  heating  in  the  arm  X  and  that  I'x  is  the  greatest 
current  which  can  be  employed  in  that  arm. 

If  a  Kelvin  galvanometer  of  the  best  resistance  is  employed 
and  the  bridge  is  out  of  balance  by  a  small'  amount,  dP,  then 
using  equations  (1),  (3),  (4)  and  the  approximate  relation 


the  deflection  of  the  galvanometer  is  given  by 

D  -  KI.  VR«  =  K          dxVx  P  .     (10) 


The  sensitiveness  which  can  be  obtained  is  seen  to  be  pro- 
portional to  the  square  root  of  the  allowable  power  loss  in  the 
arm  which  limits  the  bridge  current. 

Now  suppose  that  a  critically  damped  moving-coil  galva- 
nometer is  to  be  used. 

In  this  case  let  R'G  be  the  total  resistance  of  the  galvanometer 
branch  of  the  circuit.  R'G  will  be  made  up  of  the  resistance  of 
the  galvanometer  itself  plus  any  resistance  which  it  is  necessary  to 
add  in  order  to  bring  about  critical  damping.  Let  Rc  be  the  total 
resistance  of  the  galvanometer  circuit  which  is  required  for  critical 
damping,  then  as  the  bridge  is  nearly  balanced, 


also 
and 


+  TT~I — -\T  I    v  i — TO  =  RO  a  definite  resistance, 
M  -J~  J\  -f-  A  +  r 


M  _  X 

N  '"  P' 


Suppose  that  the  resistance  of  the  arm  P  is  increased  from 
the  value  necessary  for  a  perfect  balance  by  a  small  amount, 
dP,  then  the  galvanometer  current  becomes 


THE  MEASUREMENT  OF  RESISTANCE         189 
(JT+ 


Rc(M  +  N  +  X  +P)       RC(X  +  P) 

/1\  /5P\  n, 

=  (RC)  (P)  (7* 


and  the  deflection  is 


$  y  is  the  volt  sensitivity  of  the  galvanometer  when  it  is  critically 
damped. 

As  in  the  previous  case,  the  sensitiveness  of  the  bridge  is 
proportional  to  the  square  root  of  the  allowable  power  loss  in 
the  arm  which  limits  the  bridge  current. 

If  the  resistance  of  the  bridge  (RB)  is  so  great  that  the  gal- 
vanometer is  under-damped,  a  resistance  must  be  put  in  parallel 
with  the  bridge  between  the  galvanometer  terminals.  Let 
the  value  of  this  resistance  be  Rs  and  let  RK  be  the  resistance 
which  it  is  necessary,  in  any  case,  to  put  in  series  with  the  gal- 
vanometer in  order  to  attain  critical  damping.  That  is,  let 

RC  =  RG  +  RK- 

In  this  particular  case  RK  is  the  parallel  resistance  of  the 
bridge  and  the  resistance  with  which  it  is  shunted,  or 

P  RsRs 

~~    R^+~WB 

also 

(M  +  X)(N  +  P) 
M  +  N  +  X  +  P 

The  galvanometer  current  when  the  bridge  is  slightly  out  of 
balance  is 

T  (M  +  X)IxRs8P 

~  [Ro(Rs  +  RB)  +  RBRS](M  +  N+X  +  PJ 


The  sensitivity  is  seen  to  be  diminished  in  the  ratio  ^~- 

IlB 


190 


ELECTRICAL  MEASUREMENTS 


MEASUREMENT  OF  LOW  RESISTANCE 

Wheatstone  Bridge  Method. — When  the  value  of  X  becomes 
small,  0.1  ohm  or  less,  it  is  difficult  to  determine  it  accurately, 
owing  to  the  uncertainty  due  to  contact  resistances  introduced 
at  the  binding  posts  where  X  is  clamped  to  the  bridge.  For 
example,  such  resistance  for  a  No.  12  wire  clamped  by  a  binding 
post  may  be  about  0.00015  ohm.  Again,  all  standard  low 
resistances  and  the  shunts  used  in  current  measurements  are 
provided  with  potential  terminals,  and  the  desired  resistance  is 
that  between  the  points  where  these  terminals  are  connected 
to  the  main  resistance.  The.  following  method  of  comparing 

such  resistances  with  a  stand- 
ard is  very  useful,  since  it  re- 
quires no  special  apparatus. 

Let  it  be  required  to  meas- 
ure the  resistance  of  a  given 
length  of  the  bar  X.  Con- 
nect it  in  series  with  the 
standard  resistance,  S,  as  in- 
dicated, and  attach  two  po- 
tential terminals,  c  and  d,  at 
the  proper  points  (Fig.  107). 
These  terminals  may  be 
clamps  making  contact  with 

the  bar  by  a  pointed  screw  or  knife  edge.  In  order  to  compare 
X  and  S,  the  intermediate  resistance  between  b  and  c  must  be 
eliminated.  To  do  this  connect  the  galvanometer  at  b  and 
balance;  call  the  necessary  value  of  R,  Rb,  then 

Z?l  Q 

ri  o 


FIG.  107. — Wheatstone  bridge  method 
for  comparing  low  resistances. 


#6       X  +  a 

Now  change  the  galvanometer  wire  to  c  and  balance  again;  call 
this  value  of  R,  Rc,  then 

Re  =  ~~X~ 
a  can  be  eliminated  from  these  two  equations,  giving  as  a  result: 


THE  MEASUREMENT  OF  RESISTANCE          191 

It  has  been  assumed  that  the  resistance  a  remains  constant. 
Consequently  all  clamps  and  connections  must  be  firmly  set  up 
and  a  itself  should  be  of  so  large  a  cross-section  that  it  will  not 
heat  with    the   largest   current   which  is  used.     The  following 
points  should  be  attended  to:  the  resistance  of  a  must  be  made 
as  small  as  possible;  the  total  bridge  current  IB  should  be  as 
large  as  is  consistent   with   absence  of   heating  in  the   various 
bridge    arms;    Rl,   and    consequently    Rc    and    Rb,    should   be 
small;  their  magnitude  is  limited  by  the   fact   that    they   are 
usually  adjustable  to  single   ohms,  and  a  certain  definite  per- 
centage precision  is  usually  required  in  the  results.     They  should 
be  large  enough  so  that  there  is  no  danger  of  heating,  and  so 
large  that  the  resistances  of 
the  connection  wires  fG  and  dE 
are    negligible.     If  it  should 
prove    that    Rc    and    Rb    are 
much    smaller    than    Rl,    it 
would  be  better  to  make  the 
adjustment   by  changing  .R1 
rather     than     as     suggested 
above.     The  standard  resist- 
ance    5   should    have  ample         *"• 
current  carrying  capacity.     It 
may  be  necessary  to  keep  the  temperature  of  X  down  by  immer- 
sion in  an  oil  bath. 

Thomson  Bridge  or  Kelvin  Double  Bridge.6 — The  elimina- 
tion of  the  intermediate  resistance  a  may  also  be  accomplished 
by  means  of  the  Thomson  bridge.  The  scheme  embodied 
in  this  instrument  is  that  most  frequently  employed  for  the  pre- 
cision comparison  of  low  resistances;  it  is  also  commonly  used  for 
special  bridges  designed  for  the  rapid  measurement  of  the  con- 
ductivity of  samples  of  wire. 

Inspection  of  the  theoretical  diagram  will  show  that  this 
arrangement  differs  from  the  Wheatstone  bridge  in  the  addition 
of  two  auxiliary  resistances,  m  and  n,  which  are  placed  in  series 
and  shunted  around  the  resistance  a,  which  is  to  be  eliminated; 
one  galvanometer  terminal  is  connected  to  the  junction  of  m 
and  n.  See  Fig.  108. 

The  conditions  necessary  for  a  balance  may  be  shown  thus: 


192  ELECTRICAL  MEASUREMENTS 

Assume  that  the  galvanometer  stands  at  zero.  Between  the 
terminals  of  a  there  must  be  a  point  at  the  same  potential  as  c; 
let  d  be  this  point;  suppose  it  to  be  joined  to  c  by  a  connection  of 
zero  resistance,  thus  bringing  the  points  c  and  d  together;  this  is 
allowable  from  the  manner  of  locating  the  point  d.  The  ar- 
rangement has  then  become  a  Wheatstone  bridge  with  arms 


,   _ 

M  ,  N,  X  +  -        -  and  P  + 


ra  +  «i  n  -+-  a? 


.A.    ~\ 


•f  f  .. 

.    M  _  ra 

N 


71  +  012 

From  the  manner  of  locating  d, 

m       n  m  n 

-  =  —  or-         -=-       — 
OL\       oiz       ra  -f-  on       n  -\-  a^ 

Consequently 

nai 
M  n  +  a* 

F=^+ 

and 


MP       I     n 


(     n     \    / 
-  IrTT^/   \ai  ~  a2 


N      •  \n  +  aJ   V"1       "27V/   '      N 


/    n«2    \   /ra       M\  t 
\n  +  aa/    \n       N / 


X 


Obviously,  if  the  resistances  are  adjusted  so  that  —  ~  ~T\J  the 

MP  MP 

second  member  becomes  -^r-,  and  X  =  -^-.     The  measurement 

is  then  independent  of  a. 

For  general  laboratory  purposes  P  may  be  a  variable  standard, 
and  is  frequently  a  slide  wire  or,  better,  a  resistance  divided  into 
tenths,  the  last  tenth  being  a  slide  wire  of  perhaps  0.001  ohm. 
This  standard,  shown  diagrammatically  in  Fig.  109,  should  have 
ample  carrying  capacity,  50  amp.  at  least. 

A  convenient  form  of  this  bridge,  employing  such  a  low- 
resistance  standard,  and  adapted  to  commercial  work,  is  shown 
diagrammatically  in  Fig.  110.  In  this  arrangement  it  is  assumed 


THE  MEASUREMENT  OF  RESISTANCE 


193 


that  the  resistances  of  the  connecting  leads  cc',  dd',  ee'  and  //' 
are  so  small,  compared  with  the  resistance  with  which  they  are 
in  series,  that  their  effects  are  negligible. 

With  the  Thomson  bridge  as  it  is  actually  used,  X,  P  and  a  are 
always  small,  so  that  it  is  necessary  to  control  the  bridge  current 


O 


FIG.  109. — Variable  standard  resistance  for  use  with  Thomson  bridge. 

by  a  rheostat;  the  current  should  be  as  large  as  is  compatible  with 
accuracy.  Its  limiting  value,  and  therefore  the  sensitivity  of 
the  bridge,  is  fixed  by  the  carrying  capacity  of  the  resistances 
employed;  consequently  ample  provision  must  be  made  for  dis- 
sipating the  heat  generated  in  the  various  arms. 


I  I 

Uc x *t< cr >\* P— -H 


Rheo. 

FIG.  110. — Diagram  of  laboratory  form  of  Thomson  bridge. 

The  resistance  to  be  measured  must  be  provided  with  potential 
terminals  or  their  equivalent.  In  dealing  with  rods  the  contacts 
at  c  and  d  may  be  made  by  soldering  small  wires  across  the  rod, 
the  superfluous  solder  being  carefully  removed,  or  more  con- 
veniently, by  point  or  knife-edge  clamps. 

13 


194  ELECTRICAL  MEASUREMENTS 

With  massive  conductors  it  is  absolutely  necessary  that  the 
relative  positions  of  the  potential  and  current  terminals  be  such 
that  the  stream  lines  between  c  and  d  are  in  their  normal  posi- 
tion; for  instance,  in  measuring  a  low-resistance  shunt,  such  as  is 
used  for  large  currents  on  switchboards,  a  serious  error  may  be 
introduced,  even  if  c  and  d  are  at  the  proper  points,  if  the  current 
is  not  led  into  the  short,  heavy  terminals  exactly  as  it  is  to  be  in 
the  subsequent  use  of  the  instrument. 

Expression  for  Galvanometer  Current. — Let  the  arrangement 
of  the  conductors  and  the  mesh  currents  be  as  shown  in  Fig.  111. 
The  mesh  equations  are 

(x  +  y)(M  +  RG  +  m  +  X)  -  yRG  -  zm  -  IBX  =  0 
(y)(N  +  P  +  n  +  RG)  -  (x  +  y)Ro  -  zn  -  IBP  =  0 

(z)(m  +  n  +  a)  —  (x  +  y)m  —  yn  —  IBa  =  0. 


I 
FIG.   111.  —  Mesh  diagram  for  Thomson  bridge. 

Solving  for  x,  which  is  the  galvanometer  current,  gives: 


=  T    =    T    _  m      n       a 

B  {* 


where  [  ]  = 

na(M  +  X  +RG  )  +  ma(N  +  P  +  RG  )  +  mn(M  +N  +  X+P+  « 


ra-fn  +  a 

(14) 
If  the  galvanometer  stands  at  zero,  IG  is  zero,  and 

tm       M\ 
MP  _  a(mN  -  nM)    _  MP  _         (n  ~  W/ 

N'     Nm  +  n+a~     N         anm  +  n      a 


THE  MEASUREMENT  OF  RESISTANCE         195 

Convenience  dictates  that  the  second  term  on  the  right-hand 
side  of  the  equation  be  made  zero;  this  is  accomplished  if  m 

and  n  are  so  adjusted  that  —  =  ^-     In  other  words,  M,  N, 

Ti  1\ 

m,  n,  should  fulfil  the  conditions  for  the  resistances  in  an  ordinary 
Wheatstone  bridge,  in  which  case  X  is  independent  of  the  inter- 
mediate resistance  a  and  of  the  auxiliary  conductors  n  and  m, 
as  has  just  been  shown  in  a  somewhat  less  general  fashion. 

In  the  commercial  instrument  the  ratio  arms  are  usually 
mounted  in  the  same  box  and  are  capable  of  variation,  being 

made  up  of  coils  so  chosen  that  the  relation  —  =  -^r  is    con- 

Yl          J\ 

veniently  attained.  If  this  condition  is  not  exactly  fulfilled,  the 
error  due  to  neglecting  the  last  term  in  (15)  will  diminish  as  a  is 
decreased;  therefore  the  resistance  of  the  intermediate  con- 
nection should  be  made  as  small  as  possible,  especially  when 
measuring  small  resistances.  One  obvious  test  for  the  accuracy1 

m       M 
of  the  relation  —  =  ^r  may  be  made  by  temporarily  increasing 

a,  or  better,  by  altogether  removing  the  connection,  thus  breaking 
the  circuit.  If  the  galvanometer  remains  in  balance  with  a 
both  open  and  closed  the  adjustment  is  correct. 

Best  Resistance  for  a  Thomson  Galvanometer  When  Used 
with  a  Thomson  Bridge. — The  best  resistance  for  the  galvanome- 
ter may  be  found  as  follows:  The  resistance  a  is  always  made 
as  small  as  possible;  assume  that  it  is  negligible  in  comparison 
with  both  m  and  n,  then  [  ]  in  equation  (14)  reduces  to 


and 

(MP-  NX) 


»  +  STTIS  (M  +  N  +  x  +  p  )  +  (M  +  X](N  +  p) 

With  Thomson  galvanometers  having  coils  of  equal  dimensions 
the  relation  between  the  current,  the  resistance  and  the 
deflection  is 

D  =  K 


If  the  resistance  of  the  arm  P  differs  from  that  necessary  for 


196  ^  ELECTRICAL  MEASUREMENTS 

a  perfect  balance  by  a  small   amount,  5P,   the  galvanometer 
deflection  is 


+  N  +  X  +  P)  +  (M  +  X)(N  +  P) 

D  is  to  be  made  a  maximum  by  adjusting  RG.  On  differentiating 
and  equating  the  result  to  zero  it  will  be  found  that  the  maximum 
value  of  D  will  be  obtained  when 


mn 

=  m  +  n  +  M  +  N  +  X  +  P 

That  is,  the  galvanometer  resistance  should  be  equal  to  that  of 
the  remainder  of  the  circuit  in  which  it  is  placed. 

Sensitiveness  Attainable  in  Measurements  With  the  Thomson 
Bridge.  —  The  sensitiveness  of  the  bridge  increases  propor- 
tionally to  IB,  the  limit  being  reached  when  one  of  the  arms 
begins  to  heat  unduly.  As  the  bridge  is  usually  employed,  the 
limit  will  be  set  by  either  X  or  P. 

When  the  bridge  is  nearly  balanced  and  the  resistance  a  is 
small  compared  with  m  and  n, 

rM  +  X  .        a     i       rM 

IB  = 


If  a  Thomson  galvanometer  of  the  best  resistance  is  employed, 
the  value  for  R0  reduces  to 

P(M  +  X  +  m) 

X+P 
and 

IBMdP 


IG 


2(N  +P)(M  +  X  +  m) 
Substituting  these  values  in  the  expression  for  D  and  reducing 
gives 


If  m  =  0  this  reduces  to  equation   (10)   which  applies  to  the 
Wheatstone  bridge. 

If  the  same  conductors  M,  N,  X,  P  are  arranged  as  a  Wheat- 
stone  bridge  and  then  as  a  Thomson  bridge  it  will  be  found  from 


THE  MEASUREMENT  OF  RESISTANCE         197 

(10)  and  (17)  that  with  a  Thomson  galvanometer  the  Wheat- 
stone  bridge  arrangement  will  be  the  more  sensitive  in  the  ratio, 


=  x/l  + 


DT   "    AT    r#  +  P 

If  a  critically  damped  moving-coil  instrument  is  to  be  used 
and  the  resistance  of  the  bridge  is  so  low  that  the  instrument  is 
over-damped,  it  will  be  necessary  to  increase  the  resistance  of 
the  galvanometer  circuit.  It  will  be  assumed  that  the  resistance 
a  is  low  compared  with  m  and  n.  The  arrangement  then 
becomes  the  equivalent  of  a  Wheatstone  bridge  where  the 
resistance  of  the  galvanometer  branch  is 

R'G  =  RG  ~\ h  R 

m  +  n 

R  being  the  resistance  added  in  order  to  obtain  critical  damping. 
Let  the  resistance  of  the  circuit  necessary  for  critical  damping 
be  Rc,  then 

RC  =  RB  H~  R  G 

where 


- M+N+X+P 
When  the  bridge  is  slightly  out  of  balance 

rx(M  +  x)dp 

*<>  --=  ~(RC  _  Rg)  (M  +  N  +  X  +  P)  + 


D  =  sj0  =  sv  (~)  (i'xvx)  (Y^P)  OS) 

If  the  instrument  is  under-damped,  it  will  be  necessary  to 
place  a  shunt  around  the  bridge  between  the  galvanometer 
terminals.  In  this  case,  if  R0  is  the  resistance  of  the  galva- 
nometer and  Rs  that  of  the  shunt, 

FX(M  +  X)RS8P 
(  RG  +  RS)  +  RG  1 


198  ELECTRICAL  MEASUREMENTS 

The  bridge  resistance  is 

_mn__       (M 
s- 


[Ro  (Rs  -f  RB)  +  RSRB](M  +  N  +  X  +  P) 

The  resistance  which,  in  any  case,  it  is  necessary  to  add  to 
that  of  the  galvanometer  to  produce  critical  damping  is  RK, 
that  is, 

Re  =  RG  ~\-  RK> 

The  value  of  RK  is 

RsRa 
RS  -f-  RB 


.  I'XXRK8P 

.  .  IG  = 


and 


Compare  formula  (12)  on  page  189. 

Precision    Measurements    with    the   Thomson  Bridge.7 — In 

the  proofs  already  given  M ,  N,  m,  n,  are  the  total  resistances 
of  the  various  bridge  arms,  that  is,  they  are  the  sums  of  the 
resistances  of  the  coils  in  the  arms  and  of  the  necessary  leads. 
The  lead  resistance  can  never  be  zero;  consequently,  though  the 

coils   themselves   are    adjusted    so    that    the    relation  ^   = 

N        n 

is  fulfilled,  yet  when  they  are  connected  into  circuit  by  the 
necessary  leads  this  relation  will  be  slightly  disturbed  and  the 
elimination  of  a  from  the  results  will  not  be  complete.  In  the 
careful  comparison  of  resistance  standards  this  matter  is  of  im- 
portance, for  of  necessity  the  resistances  of  the  potential  terminals 
are  included  in  the  bridge  arms. 

If  the  resistances  in  the  arms  are  separated  into  two  parts, 
that  in  the  coils  being  denoted  by  the  subscript  c  and  that  in  the 
leads  by  the  subscript  L,  equation  (15)  becomes 

me  +  ML       Me  +  ML 

X  =P  I^-HT") xnc  +  ?L       NC  +  NL,          _    (2Q) 

*  A7        AT   '  mc  +  ™>L  +  nc  +  nL  '    - 


THE  MEASUREMENT  OF  RESISTANCE          199 

If  the  elimination  of  a  from  the  result  is  complete,  the 
balance  of  the  bridge  will  not  be  upset  when  a  is  greatly  in- 
creased or  even  made  infinity  by  breaking  the  connection 
between  X  and  P.  Therefore  the  test  for  the  proper  adjustment 
of  the  auxiliary  ratio  is  that  the  bridge  remains  in  balance  with  a 
closed  and  with  a  open.  In  precision  measurements  it  is  essential 
that  a  be  made  as  low  as  possible,  and  less  than  X. 

Reeves  Method  for  Adjusting  the  Ratio  Arms  to  Eliminate  a. 
—Based  on  the  foregoing,  the  process  of  adjustment  to  eliminate 

M 

a  is,  with  a  in  place,  to  adjust  the  main  ratio  -^  until  the  bridge 

is  balanced,  then  to  remove  a  and  rebalance  by  changing  the  ratio 

This  second  adjustment  will  throw  out  the  first,  so  a  must  be 
n 

replaced  and  -^  readjusted  and  so  on  until  by  successive  approxi- 

mations such  an  adjustment  is  attained  that  the  balance  is  main- 
tained with  a  either  closed  or  open.  This  process  of  successive 
balances  eliminates  all  questions  as  to  the  exact  values  of  m 
and  n  and  their  leads. 

When  the  elimination  of  a  is  complete, 


The  lead  resistances  to  M  and  N  must  be  determined  and  allowed 
for. 

Wenner  Method  for  Eliminating  the  Effects  of  Lead  Re- 
sistances and  a.  —  For  this  method  of  working  the  Thomson  bridge 
it  is  necessary  that  the  slides  on  the  main  and  auxiliary  ratio  arms 

be  mechanically  connected  so  that  the  relation  -^~-  =     cis  always 

1\  c        We 

maintained.     The  coils  are  adjusted  with  this  in  view. 

Inspection  of  formula  (20)  shows  that  if  in  addition  the  resist- 
ances of  the  leads  to  the  ratio  coils  are  adjusted  so  that 

MCNL  =  NCML 
and 

mcnL  =  ncmL 
then 


X  =  P 


/MC\ 
(NO) 


200  ELECTRICAL  MEASUREMENTS 

Therefore  ML  and  mL  are  made  adjustable  by  including  in  each  a 
mercury  slide  resistance  (a  and  b  in  Fig.  112).  This  consists  of 
an  ebonite  tube  about  12  cm.  long  with  a  3-mm.  bore.  The 
terminals  are  at  the  upper  and  lower  ends  of  the  tube  and  an  amal- 
gamated copper  plunger  serves  to  displace  and  short-circuit 
more  or  less  of  the  mercury.  This  form  of  adjustable  resistance 
is  remarkably  definite  in  its  action. 

To  carry  out  the  adjustment  it  is  necessary  to  add  two  switches, 
Si  and  Szj  as  shown  in  Fig.  112,  by  which  the  arms  Mc  +  Nc 
and  mc  +  nc  may  be  short-circuited. 

The  final  balance  is  attained  by  four  steps: 

1.  With  both  Si  and  $2  open, 
the  bridge  is  balanced  as  usual 
by  adjusting  the  ratio  arms. 

Mr  V^  2.  The   switch  Si  is  closed; 

the  balance  will  be  upset;  it 
is  restored  by  adjusting  ML  by 
means  of  the  rheostat  a.  This 
makes 

FIG.    112. — Wenner     arrangement      ,,  ,r          ,r  ,T  ,       , 

for  eliminating  the  effect  of  lead  re-     MLNC  =  NLMC,  very  closely, 
sistances  in  the  Thomson  bridge. 

3.  The  switch  Si  is  opened 

and  $2  is  closed  and  the  balance  restored  by  adjusting  the  value 
of  mL  by  means  of  the  rheostat  6.  This  makes 

mcnL  =  ncmL,  very  closely. 

4.  With  both  Si  and  $2  open,  the  bridge  is  finally  balanced 
by  adjusting  the  double  ratio  slides.  If  this  last  adjustment 
requires  a  considerable  change  in  the  setting  of  the  ratio  slides, 
the  adjustments  are  repeated. 

Measurement  of  Resistances  in  Permanently  Closed  Circuits. 
— For  a  method  of  measuring  a  resistance  which  is  included  in  a 
circuit  which  cannot  be  opened,  see  page  96. 

MEASUREMENT  OF  HIGH  AND  OF  INSULATION  RESISTANCE 

The  measurement  of  insulation  resistance,  using  direct- 
current  potentials  of  a  few  hundred  volts,  is  of  great  practical 
importance  because  of  its  utility  as  a  means  of  separating  the 


THE  MEASUREMENT  OF  RESISTANCE 


201 


good  from  the  defective  insulated  wires  during  the  process  of 
manufacture.  Also,  specifications  as  to  insulation  resistance  as 
measured  by  direct  currents  are  inserted  in  contracts. 

It  is  to  be  understood  that  the  results  of  this  test  are  not 
"  resistances "  in  the  same  sense  as  those  obtained  for  metallic 
conductors  by  use  of  the  Wheatstone  bridge.  As  the  test  is 
ordinarily  carried  out,  the  results  give  no  means  of  calculating 
the  current  which  will  finally  flow  through  the  insulation  of  the 
wire  under  the  prolonged  application  of  a  direct-current  electro- 
motive force  (see  page  207,  Absorption  Effects).  It  is  to  be 
understood  that  the  current  which  will  flow  through  the  di- 


FIG.  113. — Connection  for  measuring  insulation  resistance. 

electric  when  the  applied  electromotive  force  is  periodic,  es- 
pecially at  the  high  frequencies  employed  in  telephony,  involves 
a  very  different  " resistance"  from  that  determined  by  this 
method,  at  a  given  voltage  it  is  distinctly  lower,  due  to  the  energy 
dissipated  in  the  dielectric. 

Direct-deflection  Method. — Insulation  resistances  have  very 
high  values  and  may  be  several  hundred  or  several  thousand 
megohms,  a  megohm  being  1,000,000  ohms.  The  method 
usually  employed  in  these  measurements  is  really  one  of  sub- 
stitution; the  necessary  apparatus  is  shown  in  Fig.  113. 

The  galvanometer  G  should  be  of  the  D'Arsonval  type  and 
very  sensitive;  an  instrument  having  a  sensitivity  of  about 


202  ELECTRICAL  MEASUREMENTS 

1  X  109  and  of  approximately  1,000  ohms  resistance  will  be 
satisfactory.  This  galvanometer  must  have  a  good  law  of 
deflection;  that  is,  the  deflection  must  be  proportional  to  the 
current,  and  it  must  have  a  definite  zero  reading.  It  should 
be  so  supported  that  it  is  free  from  mechanical  vibration  and 
thoroughly  insulated  electrically.  C\  is  an  ordinary  four-part 
commutator  for  reversing  the  galvanometer  current,  as  it  is 
necessary  to  keep  the  deflections  in  the  same  direction  on  account 
of  possible  irregularities  of  the  zero  reading  due  to  the  coil  being 


11  Cells  of  1,000  W  each  ^-& 
11  Coils  of  200W  each 


^ 

11  Coils  of  40 W  each  Q  6  (ST57)  (5^6^66 

f     012345   87  8  9 
11  Coils  of  8  W  each 


FIG.  114. — Universal  shunt  box. 

slightly  magnetic.  The  shunt  S  should  be  of  the  Ayrton  uni- 
versal type,  for  by  selecting  one  of  the  proper  resistance  the 
galvanometer  may  be  critically  damped,  thus  enabling  the 
readings  to  be  taken  in  the  shortest  possible  time.  With  this 
type  of  shunt,  when  used  in  the  manner  indicated,  the  damping 
of  the  galvanometer  is  independent  of  the  multiplying  power, 
consequently  the  instrument  will  not  be  overdamped  even 
though  it  be  heavily  shunted.  Also,  though  there  will  usually 
be  some  thermal  electromotive  forces  due  to  inequalities  of 
temperature  in  the  galvanometer  circuit,  G,  C\,  and  S,  no  dif- 


THE  MEASUREMENT  OF  RESISTANCE         203 

ficulty  will  arise,  as  this  circuit  is  of  constant  resistance;  the  only 
effect  will  be  that  the  deflections  will  be  read  from  a  zero  which 
may  differ  slightly  from  the  mechanical  zero  of  the  instrument. 

R  is  a  fixed  known  resistance  of  100,000  ohms  or  ^0  megohm. 

An  exceedingly  convenient  form  of  Ayrton  shunt  is  shown  in 
Fig.  114.  The  constant  resistance  in  the  box  between  the  galvan- 
ometer terminals  is  10,000  ohms.  By  means  of  the  four  handles, 
the  movable  terminal  may  be  carried  from  0  to  10,000  by  steps 
each  one  of  which  changes  the  multiplying  power  by  Ko.ooo 
part  of  the  value  it  has  when  all  the  slides  are  at  the  extreme 
right  hand,  which  value  is  taken  as  unity;  for  with  the  Ayrton- 
Mather  arrangement  we  are  concerned  only  with  relative 
multiplying  powers.  The  multiplying  power  to  be  used  is 
obtained  by  dividing  10,000  by  the  sum  of  the  readings  of  the 
four  slides.  The  three  posts  at  the  rear  are  the  shunt  terminals; 
the  four  in  the  second  line  connect  with  the  resistance  R,  of 
100,000  ohms,  which  is  divided  into  three  sections  of  10,000, 
30,000  and  60,000  ohms  respectively. 

The  key  K2  (Fig.  113)  is  kept  in  the  position  shown,  by  a 
spring;  when  in  this  position  no  current  can  flow  through  the 
galvanometer  and  the  instrument  is  thoroughly  protected.  If 
the  key  be  held  in  the  dotted  position  the  galvanometer  is  in 
service.  The  construction  should  be  such  that  the  circuit  is 
not  broken  when  the  key  is  thrown  from  one  position  to  the 
other. 

The  key  KI  serves  to  throw  the  cable  in  circuit  and,  when  in  the 
position  shown,  short-circuits  it,  thus  ensuring  thorough  dis- 
charge. The  battery  B  is  connected  to  one  side  of  a  double- 
pole,  double-throw  switch  €%,  the  other  side  being  short-circuited 
to  enable  discharge  deflections  to  be  taken.  One  of  the  middle 
connections  of  C2  is  carried  to  the  tank  plate  P,  the  other  to  the 
middle  post  of  Kz.  The  battery 'should  be  fairly  well  insulated 
to  prevent  its  running  down.  It  must  be  capable  of  giving  a 
constant  e.m.f.  of,  possibly,  500  volts. 

It  is  usual  to  connect  the  negative  pole  of  the  battery  to 
the  core  of  the  cable,  the  idea  being  that  with  this  connection 
the  effect  of  electrolysis  is  to  open  up  any  fault  which  may  exist 
in  the  insulation.  Many  specifications  require  tests  with  both 


204  ELECTRICAL  MEASUREMENTS 

the  —  and  +  poles  connected  to  the  core  and  require  that  the 
two  results  check. 

To  measure  X  the  " constant"  of  the  apparatus  must  first  be 
determined;  this  is,  the  number  of  megohms  at  X  which  will 
correspond  to  a  deflection  of  1  mm.  on  the  galvanometer  scale. 
To  do  this,  short  circuit  X  at  KI  by  a  piece  of  wire  W]  the  resistance 
of  the  circuit  will  then  be  R  +  PR,  where  PR  is  the  resistance  of 
the  shunted  galvanometer,  the  leads  and  the  battery.  S  should 
be  set  at  its  smallest  value  and  the  deflection  of  the  galvanometer 
noted.  Now,  if  necessary,  alter  S  to  obtain  a  good  reading; 
call  this  DR  and  let  mR  be  the  corresponding  multiplying  power 
of  the  shunt.  Then  E  =  IR(R  +  PR).  When  X  is  in  place 
E  =  IX(X  +  R  -f  Px).  As  the  deflection  of  the  galvanometer  is 
proportional  to  the  current, 

IR  =  KmRDR, 

Ix  =  KmxDx, 
therefore  X  =  mR^R  (R  +  PB)  -  (R  +  Px). 


In  general,  R  +  Px  is  negligible  compared  with  X,  and  PR  neg- 
ligible compared  with  R]  so, 

x  =  RmRDR 


The  quantity  RmRDR  is  the  " constant"  of  the  apparatus.  As 
R  is  expressed  in  megohms,  this  is  the  number  of  megohms  for 
unit  deflection  of  the  galvanometer  when  the  relative  multiplying 
power  of  the  shunt  is  unity. 

The  resistance  R  is  left  in  circuit  continuously,  in  order  that 
there  may  be  no  possibility  of  a  current  being  sent  through  the 
galvanometer  of  sufficient  strength  to  burn  it  out.  The  mag- 
nitude of  R,  }{Q  megohm,  is  so  small  that  no  material  error  is 
introduced  by  this  procedure,  as  X  is  some  hundreds  or  thousands 
of  megohms. 

Precautions. — In  order  that  a  measurement  of  insulation 
resistance  may  possess  any  value,  one  must  be  sure  that  the 
only  current  which  passes  through  the  galvanometer  is  that  which 
flows  through  the  insulation  of  the  cable.  Therefore,  the 
galvanometer  must  be  connected  to  the  core  of  the  cable  and 


THE  MEASUREMENT  OF  RESISTANCE         205 


III 


not  to  the  tank  plate.  As  the  tank  is  grounded,  any  leakage  cur- 
rent due  to  imperfect  insulation  of  battery  and  leads  will  be 
measured  by  the  galvanometer,  if  it  be  connected  to  the  tank 
plate,  and  the  results  of  the  test  vitiated. 

Any  current  which  leaks  over  the  surface  of  the  insulation  from 
the  projecting  wire  of  the  cable  to  the  tank  will  cause  error  in 
the  results.  This  leakage  current  must  be  reduced  to  zero. 
Therefore  any  protective  covering,  such  as  braid  or  armor, 
should  be  removed  from  the  ends  of  the  wire  for  a  distance  of 
at  least  18  in.,  thus  laying  bare  the  insulating  coating.  This 
latter  should  not  be  handled  and  must  be  kept  scrupulously 
clean.  As  an  additional  safeguard,  the  insulation  should  be 
cut  back  from  the  end  of  the  wire,  as  indicated  in  Fig.  113. 
This  must  be  done  with  a  sharp,  clean 
knife,  so  as  to  leave  a  perfectly  clean 
surface  of  considerable  length  (2  or 
3  in.).  In  order  to  be  absolutely 
certain  that  all  surface  leakage  has 
been  eliminated,  recourse  should  be 
had  to  Price's  guard  wire.  This  de- 
vice is  shown  in  Fig.  115. 

A  few  turns  of  bare  and  flexible  wire 
are  closely  wrapped  around  the  insu- 
lation a  few  inches  from  its  end  so  that  they  make  perfect  con- 
tact with  it;  the  wire  is  then  carried  to  the  battery  side  of 
the  galvanometer.  The  potential  difference  between  the  core 
and  the  guard  wire  is  practically  nil,  so  that  any  leakage  will 
be  from  the  guard  wire  to  the  tank;  consequently  the  leakage 
current  will  not  be  measured  by  the  galvanometer.  The  guard 
wire  may  be  used  for  a  variety  of  purposes;  for  instance,  to  pro- 
tect the  galvanometer  lead  if  it  be  long  and  cannot  be  made  an 
air  line,  or  to  protect  a  part  or  all  of  the  testing  apparatus. 

The  shunt  S,  the  commutator  Ci,  the  galvanometer  G,  the 
resistance  R,  and  the  key  KI  must  be  thoroughly  insulated. 
They  should  all  be  mounted  on  posts  of  polished  hard  rubber  at 
least  4  in.  high,  and  may  be  protected  by  a  guard  wire.  The 
lead  from  K\  to  the  cable  should,  if  possible,  be  an  air  line. 

Even  after  all  precautions  have  been  taken,  it  will  not  do  to 
assume  that  leakage  is  not  present.  A  test  must  be  made  to 


FIG.    115.  — Diagram    for 
Price  guard  wire. 


206  ELECTRICAL  MEASUREMENTS 

determine  this  point.  To  do  this,  wire  up  exactly  as  for  a  test, 
close  Kij  then  disconnect  the  lead  from  the  cable  and  leave  it 
hanging  free.  Be  sure  not  to  introduce  a  new  source  of  error 
by  the  arrangement  for  supporting  the  free  end.  Now  throw 
on  the  battery.  If  the  e.m.f.  be  high  the  galvanometer  will 
probably  give  a  slight  deflection  and  then  settle  back  to  its 
original  reading.  If  it  does  this  the  deflection  is  due  to  the 
electrostatic  action  incident  to  charging  the  apparatus  to  a  high 
potential.  Note,  with  the  key  K^  as  shown,  if  there  is  a  perma- 
nent deflection  of  the  galvanometer  and  its  direction.  Now 
put  Kz  in  the  dotted  position  and  adjust  S  for  full  sensitiveness 
(m  =  1),  and  again  note  the  deflection  if  there  be  any.  Leakage 
may  occur  on  the  lead  between  its  free  end  and  the  shunt;  if 
so,  the  deflection  will  be  positive  in  direction  and  will  not  appear 
until  the  key  K2  is  placed  in  the  dotted  position.  S  should  be 
adjusted  so  that  m  =  1.  If  the  leakage  occurs  on  the  leads  from 
the  shunt  box  to  the  galvanometer  or  at  the  galvanometer 
terminals,  the  deflection  may  be  either  positive  or  negative,  as 
follows : 
Ground  on  left-hand  lead — 

Shunt  adjusted  f or  m  =  «>,  D  =  -\-  and  small. 
Shunt  adjusted  for  m  =  1,    D  =  -f-  and  large. 

Ground  on  right-hand  lead — 

Shunt  adjusted  for  m  =  oo }   D  =  —  and  large. 
Shunt  adjusted  for  m  =  1,    D  =  —  and  small. 

The  test  should  be  repeated  with  Ci  reversed. 

When  measuring  X  the  key  K%  must  not  be  thrown  to  the 
dotted  position  until  the  cable  is  charged  electrostatically. 
Therefore,  after  closing  JfiCi,  allow  at  least  20  sec.  to  elapse  be- 
fore throwing  K%  to  the  right;  this  will  prevent  injury  to  the 
galvanometer. 

Immersion. — After  the  specimen  has  been  immersed,  sufficient 
time  must  be  allowed  before  the  test  is  made  for  the  cable  to 
become  thoroughly  saturated,  for  moisture  to  work  into  any 
defects  that  may  exist  in  the  insulation,  and  for  the  insulation 
to  attain  the  temperature  of  the  tank.  In  practice  no  tests 
should  be  made  until  after  12  hours. 


THE  MEASUREMENT  OF  RESISTANCE 


207 


Absorption  Effects. — When  the  battery  is  first  applied  to  the 
cable  there  will  be  a  sudden  rush  of  current  due  to  the  charging 
of  the  cable  electrostatically.  Therefore  it  is  absolutely  necessary 
to  have  the  key  Kz  in  the  position  shown  when  the  circuit  is 
made,  in  order  to  prevent  possible  injury  to  the  galvanometer. 
After  the  static  charging,  a  current  flows  into  the  cable,  rapidly 
diminishing  to  a  nearly  constant  value.  This  current  furnishes 
the  " absorbed"  charge  and  includes  the  current  which  actually 
flows  through  the  insulation.  The  first  portion  diminishes 
toward  zero,  while  the  latter  tends  to  become  constant.  If 


300 
200 
100 

4 

0 

•8 

1 
1 

I 

I 

II 

R   after  1  Min, 

400    Meg-ohms  per  Mile 
1230     » 

\ 

Cl 

iar 

?e 

\ 

\ 

N 

\ 

X, 

-~—  , 

—  —  . 

, 

I 

-  ..  • 

f  r 

11  12  13  14  16  16   17  18  19  2C 

1     2    3    4     5    ( 
Time 

Curve    7  taken  a 
Curve  77  taken  a 

7891^ 
JMin. 
100 
t  105.3°  F. 
200 
t  75.2°F. 
300 

0 

7 

/ 

/* 

/ 

/ 

Discharge 

/ 

/ 

/ 

FIG.   116. — Showing  the  effect  of  time  of  electrification  on  the  galvanometer 
deflection  when  measuring  insulation  resistance. 

the  switch  C2  were  now  thrown  to  the  discharge  position  (dotted), 
Ci  reversed  (to  keep  the  deflections  in  the  same  direction),  and 
the  deflection  observed,  it  would  be  found  that  at  first  there  is 
a  sudden  rush  due  to  the  condenser  discharge  of  the  cable. 
This  is  followed  by  a  current  which  gradually  diminishes  toward 
zero,  this  latter  being  due  to  the  gradual  working  out  of  the  ab- 
sorbed charge.  The  various  phenomena  are  illustrated  by  the 
curves  shown  in  Fig.  116. 

From  the  curves  it  is  seen  that  the  apparent  resistance  of  the 
insulating  covering  is  a  function  of  the  time  of  electrification  and 
that  it  is  necessary  to  state  this  time  when  quoting  values  of  the 
insulation  resistance;  otherwise  they  possess  no  meaning.  It 
is  customary  to  calculate  the  resistance  at  the  end  of  1  min. 


208 


ELECTRICAL  MEASUREMENTS 


a 
|sooo 


ce  M 


electrification;  from  this  result  and  the  known  length  of  the 
sample  the  insulation  resistance  per  mile  or  per  1000  ft.  is 
determined. 

Effect  of  Temperature. — The  substances  classed  as  insulators 
have  very  large  negative  temperature  coefficients;  that  is,  an 
increase  of  temperature  lowers  their  resistance.  This  is  shown 
in  Fig.  117  which  gives  the  result  of  tests  on  a  sample  of  rubber- 
covered  wire.  In  this  work  it  is  customary  to  express  the  tem- 
perature in  degrees  Fahrenheit. 

For  purposes  of  comparison  it  is  necessary  to  reduce  the  results 
of  insulation  resistance  measurements  to  some  standard  temper- 
ature, 15°.5C.     This  is  usually  done 
by  dividing  the  resistances  at  the  tem- 
peratures  of   observation  by  experi- 
mentally    determined     factors,     the 
values  of  which  will  be  different  for 
different  insulating  compounds.    Con- 
sequently, the  various  reduction  fac- 
tors  quoted   in  electrical  handbooks 
should  not  be  applied  indiscriminately. 
The  great  difficulty  with  tests  for 
insulation  resistance  as    a    guide   to 
the  condition  of  underground  feeders 
after  installation,  is  the  uncertainty 
as  to  the  temperature,  due  to  the  feeders  having  been  in  use, 
or  to  the  heating  by  currents  in  neighboring  ducts. 

Insulation  Testing  by  Voltmeter. — Insulation  resistances  of 
the  magnitude  of  1  or  2  megohms  may  be  measured  by  aid  of  a 
direct-current  voltmeter  of  known  resistance.  Two  readings  are 
taken,  the  first  when  the  instrument  is  directly  across  the  line, 
the  second  when  the  line  voltage  is  applied  to  the  instrument 
and  the  unknown  resistance  in  series.  The  testing  voltage  must 
remain  constant. 

Call  the  reading  when  the  voltmeter  is  across  the  line,  DI, 
and  when  it  is  in  series  with  X,  the  unknown  resistance  D2.  Then 
if  the  resistance  of  the  voltmeter  be  Rv,  and  the  constant  of  the 
instrument  considered  as  a  current  galvanometer  be  K, 


100 


«        50      60       70      80      90 
Temperature    F. 

FIG.  117.  —  Illustrating  ef- 
fect of  temperature  on  insula- 
tion resistance. 


THE  MEASUREMENT  OF  RESISTANCE         209 


E 


Rv+X 


KD,  =  -T 


ED, 


RVD1 


If  the  power  may  be  shut  off,  this  method  lends  itself  to  the 
determination  of  the  insulation  resistance  between  the  conductors 
of  a  two-wire  distribution  circuit  and  the  ground;  that  is,  the 
water  and  gas  pipes.  Such  tests  are  necessary  when  investigat- 
ing the  wiring  of  buildings.  The  circuit  may  be  opened  by  re- 
moving the  main  fuses,  and  the  necessary  e.m.f .  obtained  by  using 
either  the  supply  voltage  or  a  portable  battery  of  dry  cells. 

Loss  of  Charge  Method. — The  loss  of  charge  method  of 
measuring  insulation  resistance  is  based  on  the  following 
considerations. 

If  a  perfect  condenser  is  charged  and  then  discharged  through 

t_ 

a   resistance,   it   can   be   shown    that    Vt  =  VQe   CR  where  Fo 

is  the  initial  P.D.  of  the  plates,  Vt  the  P.D.  at  any  subsequent 
time  t,   C  and  R  the  capacity  of  the 
condenser  and  resistance  of  the  circuit. 
Solving  this  for  R, 


R  = 


Cloge^° 


£0.4343 
Vt 


400 

\ 

R= 

1000 

_/-l_ 

^300 

\ 

Vf 

0.1 
500 

V. 

2  200 

\ 

^100 

'x 

V^ 

0 

— 

60    90  120  150  180 
Time-Sec. 


FIG.  1 18. — Illustrating 
fall  of  potential  in  loss  of 
charge  method  for  measur- 
ing insulation  resistance. 


The  relation  of  its  units  is  such  that  if 
C  is  in  microfarads,  and  t  in  seconds, 
R  will  be  given  in  megohms.  If  R  be 
large,  several  hundred  or  thousand 
megohms,  the  time  of  discharge  will  be  sufficiently  prolonged, 
so  that  it  is  possible  to  follow  the  variation  of  Vt  with  an  elec- 
trometer or  electrostatic  voltmeter.  From  the  above  it  is  seen 
that  it  is  possible  to  measure  a  large  resistance  by  discharging 
through  it  a  condenser  of  known  capacity  and  noting  the  P.D. 
at  the  beginning  and  end  of  a  time  t. 

The    curve    illustrates   the   phenomena  for   the   case   where 
R  =  1,000  megohms,  C  =  0.1  microfarad,  F0  =  500  volts. 

If  the  resistance  be  exceedingly  high,  the  P.D.  of  the  condenser 
may  fall   so   slowly  that  in  any  reasonable  time,  Vt  may  not 

14 


210  ELECTRICAL  MEASUREMENTS 

differ  greatly  from  F0,  and   consequently    the   ratio  - --  will  be 

seriously  affected  by  errors  of  observation.  By  observing  F0 
and  the  fall  of  potential,  much  more  accurate  results  may  be 
obtained.  Let  the  fall  from  F0  in  time  t  be  denoted  by  v,  then 

Fo  =  7,  +  v, 
and 

Z0.4343 


R  = 


1  ^ 

loglO  -FT— 


Only  the  ratio  of  voltages  enters  the  formula,  and  it  is  possible  to 
use  a  ballistic  galvanometer  instead  of  an  electrometer  or  elec- 
trostatic voltmeter  in  the  work.  Connections  are  made  so  that 
the  condenser  is  charged  from  the  battery  through  the  ballistic 
galvanometer.  Let  the  elongation  be  Z)0  =  KQ0  =  KCVo.  After 
the  cable  has  leaked  for  t  seconds,  it  is  again  connected  to  the 
battery  through  the  galvanometer  and  the  elongation  due  to 
the  quantity  which  is  necessary  to  replace  that  which  has  leaked 
out  is  observed.  Call  this  elongation  Dt,  then 

Dt  =  KQt  =  KCv 
consequently 

J0.4343 


R  =  - 

C  logio 


D0  -Dt 


In  this  formula  an  error  in  D0  does  not  seriously  affect  the  results, 
as  it  occurs  both  in  the  numerator  and  denominator,  and  Dt  is  a 
comparatively  small  quantity  directly  observed,  so  inaccuracies 
in  it  will  not  greatly  affect  the  results.  The  ballistic  galvanometer 
should  be  so  sensitive  that  Dt  will  be  large,  and  conse- 
quently can  be  read  with  accuracy.  This  will  probably  mean 
that  the  instrument  is  used  with  the  Aryton  shunt  adjusted 
for  m  =  I.  When  D0  is  observed,  it  will  be  necessary  to  shunt 
the  galvanometer  (the  Ayrton  shunt  is  used  as  it  keeps  the  damp- 
ing constant)  in  order,  to  keep  the  deflection  on  the  scale.  In 
this  case  D0  and  Dt  are  the  deflections  corrected  for  the  multiply- 
ing power  of  the  shunts;  that  is,  both  are  reduced  to  the  value 
they  would  have  if  m  =  1. 


THE  MEASUREMENT  OF  RESISTANCE         211 

To  apply  this  method  to  the  determination  of  insulation  re- 
sistance, the  connections  shown  in  Fig.  119  are  required. 

Care  should  be  taken  that  the  connections  are  such  that  the 
current  necessary  to  charge  the  wiring  does  not  pass  through  the 
galvanometer;  the  connection  from  KI  to  the  core  should  be  short. 
Air  lines  should  be  used  when  possible. 

It  is  first  necessary  to  determine  the  capacity  of  the  cable  C,  for 
as  a  matter  of  convenience  the  cable  is  charged  and  allowed  to 
leak  through  its  own  insulation  resistance.  The  measurement  is 
made  by  the  direct  deflection  method;  KI  is  placed  in  the  mid- 
position;  by  throwing  K3  to  the  right  the  condenser  C\  is  charged 


FIG.   119. — Connections  for  measuring  insulation  resistance  by  loss  of 
charge  method. 

through  the  galvanometer,  and  the  elongation  noted.  When 
the  key  is  against  the  left-hand  stop  the  condenser  is  discharged. 
The  key  KI  is  now  thrown  to  the  position  shown,  thus  making 
sure  that  the  cable  is  discharged.  The  elongation,  D0,  on  charg- 
ing the  cable  is  now  taken  by  throwing  KI  to  the  right;  several 
observations  should  be  made;  between  them  the  cable  should  be 
short-circuited  long  enough  to  ensure  its  thorough  discharge. 
The  elongation  DQ  is  used  both  in  computing  the  capacity  C 
and  the  resistance  R.  To  determine  Dt  charge  the  cable,  and  at 
a  noted  minute  and  second,  place  KI  in  the  mid-position,  thus 


212  ELECTRICAL  MEASUREMENTS 

insulating  the  cable  and  allowing  it  to  discharge  by  leakage 
through  its  own  insulation  resistance.  At  a  noted  minute  and 
second  again  charge  the  cable,  noting  the  elongation  Dt,  which 
is  due  to  the  passage  of  the  quantity  Qt  through  the  galvanom- 
eter to  replace  that  which  has  leaked  out. 

In  thus  applying  the  loss  of  charge  method  to  cables,  the  as- 
sumption has  been  made  that  the  current  flow  through  the  in- 
sulating covering  obeys  Ohm's  law.  On  account  of  the  non- 
fulfilment  of  the  assumed  conditions,  the  results  are  subject 
to  errors;  but  in  many  cases  of  industrial  testing  the  results 
attained  by  a  definite  method  of  procedure  are  sufficient. 

It  will  be  noticed  that  for  a  given  value  of  ^  the  time  of  dis- 
charge is  proportional  to  C.  In  general,  the  capacity  of  the  cable 
is  great  enough  to  sufficiently  prolong  the  discharge;  however, 
when  short  lengths  are  tested  it  may  be  necessary  to  employ  an 
auxiliary  condenser.  If  this  be  done,  a  special  determination 
of  its  effective  resistance  must  be  made.  The  condenser  being  in 

parallel  with  the  cable,  it  is  customary 
to  compute  the  resistance  of  the  latter 
from  their  combined  resistances  by 
the  law  of  divided  circuits.  From 
what  has  been  stated  it  will  be  seen 
that  this  procedure  cannot  be  expect- 
ed to  give  results  of  great  accuracy. 

FIG.  120. — Connections  for        Loss    of    Charge    Method,    Using 

Quadrant  Electrometer.-The  fall  of 
potential  may  also  be  obtained  by 
the  use  of  a  quadrant  electrometer,  the  needle  of  which  is  charged 
to  a  high  and  constant  potential.  The  connections  are  shown 
in  Fig.  120. 

By  closing  the  switch  S  the  cable  is  charged  and  both  sets 
of  quadrants  brought  to  the  same  potential.  The  electrometer 
will  therefore  remain  undeflected.  When  S  is  opened,  the 
right-hand  quadrants  are  kept  at  a  potential  VQ  by  the  battery, 
while  the  potential  of 'the  left-hand  quadrants  gradually  falls, 
as  the  cable  discharges  through  its  own  resistance.  A  deflec- 
tion appears  which  is  sensibly  proportional  to  v. 


THE  MEASUREMENT  OF  RESISTANCE 


213 


Evershed  "Megger." — It  is  highly  desirable  to  have  some 
convenient  portable  instrument  for  measuring  insulation  re- 
sistance, which  shall  be  rugged  in  construction,  direct  reading, 
capable  of  giving  results  with  rapidity  and  so  simple  in  manipu- 
lation that  it  may  be  employed  by  persons  not  accustomed  to 
the  use  of  delicate  instruments.  In  addition,  the  device  must  be 
capable  of  furnishing  a  testing  voltage  so  high  that  it  will  search 
out  defects  of  high  resistance. 


FIG.  121. — Evershed  Megger. 

The  Evershed  Megger,  Fig.  121,  was  designed  with  these  require- 
ments in  view. 

Referring  to  the  scheme  of  connections,  M  and  M  are  permanent 
magnets  which  furnish  the  fields  both  for  the  instrument  proper 
and  for  the  small  hand-driven  magneto  D,  which  gives  the  testing 
voltage.  The  movable  element  consists  of  the  coils  BBr  and 
A  which  are  rigidly  connected;  flexible  leads  are  taken  to  the 
coils  but  there  are  no  controlling  springs. 


214  ELECTRICAL  MEASUREMENTS 

The  coils  BB'  are  in  series  and  together  with  a  suitable  re- 
sistance are  connected  across  the  terminals  of  the  magneto  D. 
The  coil  A  is  so  connected  that  it  is  traversed  by  any  current 
which  flows  through  the  specimen  when  the  latter  is  joined  be- 
tween the  external  terminals.  If  the  external  circuit  is  open, 
the  movable  element,  under  the  action  of  the  current  through  R, 
will  take  up  such  a  position  that  the  plane  of  the  coils  BB1  coincides 
with  the  dotted  line.  This  position  corresponds  to  an  infinite 
external  resistance  and  is  marked  infinity  on  the  scale.  If  there 
be  a  current  in  the  external  circuit,  due  to  the  imperfect  insulation 
resistance  of  the  specimen,  a  current  will  flow  through  the  coil 
A  and  in  such  a  direction  that  it  turns  the  movable  system 
toward  the  right,  carrying  the  coils  BB'  with  it  until  the  latter, 
which  move  in  a  non-uniform  field,  are  in  a  field  so  strong  that 
the  turning  moments  due  to  A  and  BB'  are  balanced.  The 
coil  A  may  thus  be  considered  to  furnish  the  directive  moment 
which  acts  on  the  system. 

The  indications  are  independent  of  the  voltage  of  the  magneto, 
for  if  that  changes  both  the  deflective  and  directive  moments  are 
altered  in  the  same  ratio. 

In  one  design  of  the  instrument,  the  magneto  is  driven  through 
a  clutch  arrangement  controlled  by  a  centrifugal  governor  so  that 
the  voltage  cannot  rise  above  a  definite  maximum;  then,  when 
the  crank  is  turned  fast  enough,  a  constant  testing  voltage  is 
obtained.  This  is  of  importance  when  apparatus  having  a 
considerable  electrostatic  capacity  is  tested. 

MEASUREMENT   OF   INSULATION  RESISTANCES    OF   COMMER- 
CIAL CIRCUITS  WHEN  POWER  IS  ON 

It  is  sometimes  necessary  to  measure  the  insulation  resistance 
to  " ground"  (the  water  and  gas  pipes)  of  a  distribution  system, 
for  instance,  that  of  an  office  building,  where  the  conditions  are 
such  that  the  power  is  on  and  the  supply  must  not  be  interrupted. 
This  case  is  illustrated  by  Fig.  122. 

Voltmeter  Method. — -The  resistances  to  ground  will  be  repre- 
sented by  xr  and  x^. 

If  the  insulation  resistances  are  not  above  1  or  2  megohms, 
recourse  may  be  had  to  the  voltmeter  method  (page  208).  Three 
voltage  measurements  suffice  to  determine  both  xl  and  x . 


THE  MEASUREMENT  OF  RESISTANCE 


215 


The  supply  voltage  should  be  constant  and  the  readings  made 
as  expeditiously  as  possible.  First  measure  E,  the  supply  volt- 
age, then  Vi  and  F2,  the  voltages  to  ground  from  leads  1  and  2. 
When  the  voltmeter  is  connected  from  lead  1  to  ground, 
the  voltage  E  sends  a  current,  Ji,  through  the  resistance  x2  plus 
the  paralell  resistance  of  xl  and  the  voltmeter.  Then  if  Rv  is 
the  voltmeter  resistance, 


x,Ry 

*2  +  x^+'Rv 

^i  ' 

•         1 

,{ 

A 

i 

X, 

i      _ 

v1 

I1 

Water  or  Gas  Pipe 

D 

FIG.  122. 

Similarly,  when  the  voltmeter  is  between  lead  2  and  the  ground, 

E 


also 


Hence  :- 
and 


x.,  = 


=  Rv  (^— ft— -) 

-  F,  -  1 


As  the  voltages  enter  as  a  ratio,  any  galvanometer  which 
gives  a  deflection  proportional  to  the  current  through  it  may 
be  used  in  place  of  the  voltmeter,  a  suitable  series  resistance 
being  employed.  In  this  case,  the  scale  readings  may  be  used 
in  place  of  the  voltages.  Inspection  of  the  formulae  shows  that 
the  method  is  not  applicable  when  one  side  of  the  circuit  is 
grounded.  The  method  may  be  used  to  measure  the  insulation 


216 


ELECTRICAL  MEASUREMENTS 


resistances  of  two  insulators  which  are  used  in  series;  for 
instance,  a  trolley  wire  insulator  and  its  accompanying  strain 
insulator. 

Northrup  Method. — If  the  insulation  resistances  are  too 
high  for  the  voltmeter  method,  a  galvanometer  may  be  used 
according  to  a  scheme  due  to  Northrup.11 

The  connections  are  shown  in  Fig.  123. 

A  fairly  high  resistance,  ab,  which  is  provided  with  a  sliding 
tap,  s,  is  placed  across  the  circuit.  The  galvanometer  G  is 
shunted,  preferably  by  an  Ayrton  shunt  as  shown,  so  that  its 
sensitivity  may  be  varied  to  suit  the  conditions. 


FIG.  123. — Northrup  connections  for  measuring  resistance  to  ground  when 
power  is  on. 

When  the  key  K  is  against  the  back  stop,  connection  is  es- 
tablished between  the  ground  and  s.  By  moving  s,  a  position 
may  be  found  where  the  galvanometer  will  stand  at  zero,  the 
potential  of  s  being  that  of  the  ground.  It  will  be  seen  that 
this  is  a  Wheatstone  bridge  arrangement.  Consequently 


and 


a  +  b 


If  the  key  be  depressed,  any  deflection  will  be  due  to  the  current 
from  the  battery  B  which  flows  to  s  and  there  divides,  part  going 


THE  MEASUREMENT  OF  RESISTANCE         217 

through  the  resistances  a  +  x2  and  part  through  b  +  xiy  and 
back  to  the  battery  via  the  ground  connection. 
The  total  resistance  encountered  will  be 

R  =  RG  + 


, 
~r  j— ; 


a  +  x2       b  +  x, 
RG,  a  and  b  are  negligible  with  respect  to  xl  and  x2,  so 

R  =  — l—L-  very  approximately. 


6 


If  the  voltage  of  the  battery  B  is  E,  then 


I0  =  |  -  KD 

where  K  is  the  current  necessary  for  unit  deflection  of  the  galva- 
nometer and  D  is  the  deflection. 
Then 


7? 
H'"KD 


a  +  b\ 

a  ) 


KD\ 

E  /a-f 
x*  =]O)V6 

Changes  in  circuit  conditions,  such  as  throwing  on  or  off  ap- 
pliances not  perfectly  insulated,  will  change  xl  and  xz  and  shift 
the  neutral  point.  This  may  introduce  difficulties  in  the  execu- 
tion of  the  test. 

Other  Methods  of  Measuring  Resistance  to  Ground. — 
The  current  which  flows  to  ground  from  one  of  the  line  wires 
may  be  measured  by  the  method  given  on  page  94  for  meas- 
uring the  current  in  a  permanently  closed  circuit.  The  con- 
nections are  shown  in  Fig.  124.  By  varying  r2  the  P.D.  between 


218  ELECTRICAL  MEASUREMENTS 

the  points  a  and  b  may  be  made  zero;  when  this  adjustment  is 
complete  the  deflection  of  the  galvanometer  G  is  zero  and  the 
current  which  then  flows  through  x2  is  given  by  the  galvanom- 
eter (r2.     It  follows  that 


E  _Er 

h  ":  E, 


t  Mance's  method,  originally 

designed  for  measuring  the  in- 
ternal resistance  of  batteries, 

—  may  be  so  modified  that  it  can 

FIG.   124.— Connections  for  measuring  also  be  used  for  measuring  in- 
resistance  to  ground.  sulation  resistances  while  under 

the  working  voltage. 

THE  TEMPERATURE  COEFFICIENT  OF  ELECTRICAL  RESISTANCE 

The  effect  of  change  of  temperature  on  the  electrical  resistance 
of  various  materials  is  shown  in  Fig.  125.  It  is  seen  that,  with 
few  exceptions,  the  resistance  increases  with  increase  of  tem- 
perature. For  pure  metals  an  approximate  figure  is  0.4  per  cent, 
per  degree  C.  It  may  be  noted  that  metals  which,  at  certain 
temperatures,  undergo  changes  of  structure,  for  instance,  iron 
at  about  780°C.,  show  alterations  of  curvature  in  the  temperature- 
resistance  curve  at  those  points. 

From  this  it  is  obvious  that  if  a  statement  of  an  electrical 
resistance  is  to  possess  definiteness,  the  temperature  at  which  the 
measurement  was  made  must  be  given.  Also,  when  a  resistance 
is  measured,  it  is  necessary  to  know  tKe  temperature  and  tem- 
perature coefficient  of  the  coils  with  which  it  is  compared,  as 
well  as  their  value  at  some  particular  temperature,  in  order  that 
their  true  resistance  at  the  time  of  use  may  be  known. 

Experiments  show  that,  in  general,  when  the  temperature  is 
altered,  the  change  of  the  electrical  resistance  of  a  conductor  to 
which  terminals  are  rigidly  attached,  and  which  therefore  pos- 
sesses a  constant  mass,  is  not  quite  linear;  that  is,  the  plot  con- 
necting resistance  and  temperature  is  not  exactly  a  straight  line. 
For  the  ordinary  ranges  of  atmospheric  temperatures  the  curva- 
ture is  very  slight,  but  may  be  considerable  if  the  temperature 
be  carried  to  high  values. 


THE  MEASUREMENT  OF  RESISTANCE         219 


50,000 


—  50,000 


45,000 


40,000 


35,000 


30,000 


VARIATION  OF 
Bv? ELECTRICAL  RESISTANCE  OF  PURE  METALS 


250°  200°  150°  100°  50°   0°   50°  100°  150°  200 

Temperature  in  Platinum  Degrees 
FIG.  125. — Showing  effect  of  temperature  on  electrical  resistance. 


220 


ELECTRICAL  MEASUREMENTS 


In  this  and  similar  cases,  an  empirical  relation  of  the  form  here 
given  is  frequently  employed  to  represent  the  results  of  physical 
measurements : 

Rt  =  JRoU  +  at  +  bt*  +  d»  +  .    .    .   ).  (21) 

Rt  is  the  resistance  at  t°,  and  R0  that  at  0°.  The  departure  from 
a  straight  line  is  determined  by  the  constants  b  and  c.  For  the 
special  case  of  copper,  the  variation  of  which  is  linear,  between 


16 
15 
14 
13 

12 

a11 
010 


VARIATION  OF  RESISTANCE 

OF  PLATINUM 
WITH  TEMPERATURE 


•-SH 

!i 

[Bo 


200 


400          600  800 

Temperature  (Gras  Scale) 


1000         1200 


FIG.   126. — Temperature-resistance  curve  of  platinum. 

10°  and  100°C.,  the  constants  b  and  c  are  zero.  The  constants 
a,  6,  c  are  best  determined  by  applying  the  method  of  least  squares 
to  a  series  of  measurements  of  the  resistance  made  at  different 
temperatures. 

The  temperature-resistance  curve  for  a  coil  of  very  pure  plati- 
num is  shown  in  Fig.  126;  it  is  represented  by  the  following 
equation. 

Rt  =  R0(l  +  0.00392J  -  0.00000058&2) ; 


THE  MEASUREMENT  OF  RESISTANCE         221 

therefore 

a  =  +  0.00392 

b  =  -  0.000000588. 

On  account  of  its  use  in  resistance  thermometers,  the  variation  of 
the  resistance  of  platinum  with  temperature  is  important. 

Mean   Temperature   Coefficient.  —  Denoting   particular   tern-. 
peratures  by  subscripts,  it  is  usual  to  write  formula  21  thus 

Rtl  =  #o(l  +  frfi)  (21a) 

where 


=  a  +  bti  +  ct 


It  will  be  seen  that  0^  is  the  mean,  or  average  fractional  rate  of 
increase  of  resistance  per  degree  between  0°  and  fa,  referred  to 
the  resistance  at  0°,  for 


Pti  is  called  the  mean  temperature  coefficient  of  resistance  increase. 
To  compute  the  value  of  a  resistance  at  any  temperature,  t°, 
from  that  at  some  given  temperature,  t°i, 

Rtl  =  Ro(l  +  /VO; 

Rt    =  R0(l  +  W); 
therefore 

Rt  =  Rti  i    i   /o  /  (22) 

1  +  pijii 

Temperature  Coefficient  of  Resistance.  —  As  in  general  the 
graph  connecting  Rt  and  t  is  curved,  the  true  rate  of  increase  of 
resistance  will  have  a  particular  value  at  each  temperature, 
consequently  a  very  small  temperature  interval  must  be  used  in 
computing  it. 

The  temperature  coefficient  of  resistance  increase  at  any  tem- 
perature is  the  fractional  rate  of  increase  of  resistance  for  a 
very  small  temperature  increment  referred  to  the  resistance  at 
that  temperature.  It  will  be  denoted  by  «;  then 

l_  (dRi\  a  +  2b<!  +  3c<!2  +    .    .   . 

atl  ~  Rtl  \  dt  I  tl  "  1  +  at,  +  6*!2  +  c*i«  +  .   .   . 

Rti  +A<  —  Rti 
ati  =      ~~~  ---  approximately. 


222  ELECTRICAL  MEASUREMENTS 

For  a  small  finite  temperature  interval,  A£  =  t  —  ti, 

Rt  =  Rtl(l  +  <xtl[t  -  t,]).  (24) 

On  account  of  the  approximations  involved,  equation  (24) 
applies  in  general  only  to  short  ranges  of  temperature. 

Strictly  speaking,  in  order  to  compute  a  or  ft  one  must  know  the 
values  of  the  constants  a,  6,  and  c  for  the  particular  sample  of 
material  under  discussion;  such  data  are  rarely  at  hand. 

Special  Case:  Temperature  Correction  for  Copper. — Careful 
experiments  made  at  the  Bureau  of  Standards12  upon  com- 
mercial copper  of  high  conductivity,  such  as  is  used  for  electrical 
purposes  (varying  from  96  per  cent,  to  101  per  cent,  conduc- 
tivity), show  that  between  10°  and  100°C.  the  variation  of  re- 
sistance with  temperature  is  linear,  and  also  that  the  temperature 
coefficient  at  20°  is  directly  proportional  to  the  per  cent, 
conductivity. 
That  is, 

«20  =  ^[7^201  =  0'00393  X  (Per  cent"  conductivity)  (25) 

In  this  formula  the  per  cent,  conductivity  is  expressed  decimally. 
The  temperature  coefficient  of  resistance  at  any  other  temperature 
may  be  calculated  from  that  at  20°  as  follows,  the  variation  of 
resistance  being  linear: 

!_  /dRt\  a  1 

at  ~  Rt  \  dt  /  t  ~  1  +  at  ~  1          ' 

similarly  , 

at> =  r~ 

and  a 

I        JL_    _      . 

a 

.'.  at  = 


<*, 

Let  the  original  temperature  of  reference,  t\,  be  taken  as  20°;  then 


1  +[^-201  (26) 

0.00393  X  (per  cent,    cond.)  ^ 


THE  MEASUREMENT  OF  RESISTANCE 


223 


As  the  resistance  variation  of  copper  is  linear,  measurements  to 
determine  atl  may  be  made  at  any  two  temperatures  which  may 
both  differ  from  ti,  the  temperature  of  reference;  for  let  the 
measurements  be  made  at  temperatures  t%  and  t3,  then 

D      .   z>  (^3  ~  #0  r. 


and 


Ott,    = 


By  use  of  (25)  and  (26)  the  following  table  has  been  calculated. 
The  standard  100  per  cent,  conductivity  copper  is  taken  as  hav- 
ing a  resistivity  of  0.15328  ohm  (meter,  gram)  at  20°C.  (see 
page  230). 

TABLE. — TEMPERATURE  COEFFICIENTS  OF  STANDARD  ANNEALED  COPPER  AT 
VARIOUS  TEMPERATURES  OF  REFERENCE 


Ohms 
(meter  gm.) 
at  2'0°  C. 

Per  cent, 
conduc- 
tivity 

"o 

"16 

*„ 

"25 

"30 

«50 

Inferred 
absolute 
zero.     T. 

0.16134 

95.0 

0.00403 

0  .  00380 

0.00373 

0.00367 

0  .  00360 

0.00336 

-247.8 

0.15966 

96.0 

0  .  00408 

0.00385 

0.00377 

0  .  00370 

0.00364 

0  .  00339 

-245.1 

0.15802 

97.0 

0.00413 

0  .  00389 

0.00381 

0.00374 

0.00367 

0.00342 

-242.3 

0.15753 

97.3 

0.00414 

0.00390 

0.00382 

0.00375 

0  .  00368 

0.00343 

-241.5 

0.15640 

98.0 

0.00417 

0.00393 

0.00385 

0.00378 

0.00371 

0.00345 

-239.6 

0.15482 

99.0 

0.00422 

0.00397 

0.00389 

0.00382 

0.00374 

0.00348 

-237.0 

0.15328 

100.0 

0.00427 

0.00401 

0.00393 

0.00385 

0.00378 

0.00352 

-234.5 

0.15176 

101.0 

0.00431 

0  .  00405 

0.00397 

0.00389 

0.00382 

0.00355 

-231.9 

Experiments  have  shown  that  distortions  of  the  wire,  such  as 
occur  in  winding  and  ordinary  handling,  do  not  alter  the  tem- 
perature coefficient. 

For  windings  in  general,  annealed  copper,  conductivity  100 
per  cent.,  may  be  assumed.  Hard-drawn  copper  may  be  assumed 
to  have  a  conductivity  of  97.3  per  cent.  These  values  are 
approximations  to  be  used  only  when  data  concerning  the  copper 
in  question  cannot  be  obtained. 

Measurement  of  Rise  of  Temperature. — In  the  testing  of' 
electrical  machinery  it  is  customary  to  find  the  average  rise  of 
temperature  of  copper  windings  by  measurements  of  their 


224  ELECTRICAL  MEASUREMENTS 

resistance.  This  is  facilitated  by  the  linear  relation  between 
temperature  and  resistance;  for,  assume  that  this  relation  holds 
for  all  temperature  intervals,  and  prolong  the  line  connecting 
temperature  and  resistance  downward.  It  will  cut  the  axis  of 
temperatures  to  the  left  of  the  origin  at  a  temperature  —  T°. 
Now  let  Rtl  and  Rt2  be  the  resistances  of  the  windings  at  tem- 
peratures ii  and  tz,  then 

Rt,  —  Rt!  _     Rt! 

t*-ti      ~~  T  +  ti 
or 

b  -  <i  =  (Rtt~  Rtl)  (T  +  «J-  (27) 

Rtl 

Again  from  the  above, 


*         ..  _, 
Rtl=         h  T 

The  quantity  T  is  usually  called  the  "inferred  absolute  zero." 
It  may  be  calculated  from  the  data  given  in  the  table.  For 
example, 

Rt  =  #20(1  +  <*2o[t  -  20]) 

if  the  resistance  becomes  zero  and  100  per  cent,  conductivity  be 
taken. 

*  ~  20  ^-  —  -  -  0-00^  =  --  254.5; 

.'.  T  =  -  234.5. 

These  values  are  entered  in  the  last  column  of  the  table  on 
page  223.  When  used  in  the  above  formulae  the  minus  sign  is 
omitted. 

The  Resistance  Pyrometer.13  —  Following  a  suggestion  made 
in  1871  by  W.  Siemens,  the  variation  of  the  electrical  resist- 
ance of  platinum  with  temperature  is  utilized  in  pyrometry. 
The  first  experiments  in  this  direction  were  not  successful,  and 
in  1874  the  British  Associaton  report  on  the  instruments  sub- 
mitted was  not  favorable,  it  being  found  that  after  exposure  to  a 
high  temperature  the  platinum  coils  did  not  return  to  their 
original  resistances  and  that  the  changes  were  progressive.  In 
1886  Callendar  proved  that  these  changes  were  due  to  the  ab- 
sorption by  the  platinum  of  silica  from  the  coil  support  and  of 


THE  MEASUREMENT  OF  RESISTANCE         225 

furnace  gases  which  at  high  temperatures  penetrated  the  iron 
tubes  then  employed  to  protect  the  resistance  coils.  In  view 
of  these  facts,  the  coils  are  now  wound  on  very  light  frames  of 
mica,  which  touch  each  turn  of  the  wire  at  only  four  points;  the 
areas  of  the  surfaces  of  contact  are  thus  reduced  to  a  minimum. 
The  coils  are  now  protected  by  porcelain  tubes  glazed  externally. 

In  order  to  make  the  relation  of  resistance  to  temperature 
comparatively  simple  and  one  which  may  be  determined  by 
measurements  at  three  known  temperatures,  pure  platinum 
must  be  employed. 

If  the  resistance  of  the  coil  be  measured  at  0°  and  at  100°C., 
the  average  change  per  degree  will  be 


100 
and  if  R  be  the  resistance  at  some  other  temperature, 

R  —  RQ 


100 


—  Rf 


will  be  the  corresponding  temperature,  on  the  assumption  that 
the  change  of  resistance  is  linear.  A  temperature  so  defined  is 
called  the  "  platinum  temperature,"  so 


Callendar  showed  that  for  high  temperature  measurements  it 
was  not  correct  to  assume  a  linear  variation  of  the  resistance, 
but  that  a  correction  must  be  applied  in  order  to  give  the  proper 
temperature  on  the  scale  of  the  gas  thermometer.  He  found  that 
if  t  be  the  temperature  on  that  scale,  the  difference  of  i  and  tp 
could  be  expressed  by  the  following  empirical  relation: 


where  if  pure  platinum  be  used  5  is  a  constant,  its  value  being 
about  1.505.  This  form  of  expression  holds  with  great  exactness 
for  pure  platinum,  but  is  not^  general;  for  instance,  it  fails  in  the 
case  of  palladium.  For  impure  platinum  6  must  be  expressed 
thus:  d  =  a  +  bt. 

15 


226 


ELECTRICAL  MEASUREMENTS 


To  determine  5,  pure  platinum  being  used,  the  resistance  must 
be  measured  'at  three  known  temperatures,  which  for  high  tem- 
perature measurements  are  usually  taken  as  0°,  100°,  and  444°. 70, 
the  latter  being  the  boiling  point  of  sulphur  under  carefully  speci- 
fied conditions,  this  having  been  determined  with  great  care  by 
many  experimenters.  With  the  5  correction  applied,  the  plati- 
num thermometer  reproduces  temperatures  on  the  gas  (nitrogen) 
thermometer  scale  to  within  the  limits  of  accuracy  of  the  latter 
between  -80°  and  +1,100°C. 

The  above  empirical  formula  does  not  admit  of  extrapolation 
downward  below  — 100°,  so  for  measurements  of  extremely  low 
temperatures  the  formula  must  either  be  modified  or  the  coil 


Compensating  Leads    | 
Coil  Leads 


FIG.  127.  —  Bridge  connections  for  resistance  pyrometers. 


resistance  taken  at  such  points  as  the  temperature  of  melting 
ice,  solid  CC>2,  and  the  boiling  point  of  oxygen,  in  order  that  the 
extrapolation  may  not  be  so  excessive.  The  platinum  thermome- 
ter, when  used  for  precise  work  at  high  temperatures,  must 
be  frequently  calibrated;  the  purer  the  platinum,  the  less  the 
likelihood  of  a  change  in  its  constants.  Also  the  changes  in  the 
coils  are  minimized  if  the  wire  be  large  and  be  supported  free 
from  strains.  Annealing  at  a  temperature  above  that  at  which 
the  instrument  is  to  be  used  contributes  to  constancy. 

The  coil  and  the  bridge  connections  for  measuring  the  resist- 
ance are  shown  in  Fig.  127. 


THE  MEASUREMENT  OF  RESISTANCE          227 

To  compensate  for  the  changes  in  the  resistance  of  the  coil 
leads,  due  to  temperature,  compensating  leads  as  nearly  like  the 
coil  leads  as  possible  and  in  a  similar  environment  are  inserted 
in  the  adjustable  bridge  arm,  or  three  leads  are  used  as  shown  at 
the  right  hand  of  Fig.  127. 

RESISTIVITY,  CONDUCTIVITY 

It  is  well  known  that  the  electrical  resistances  of  conductors 
having  the  same  dimensions,  but  made  of  different  materials, 
will  differ.  Each  metal  has  its  characteristic  resistance,  which, 
when  determined  for  some  unit  specimen  of  the  material  and  at  a 
stated  temperature,  gives  the  resistivity  or  specific  resistance. 
Various  methods  of  expressing  this  property  are  used;  the  three 
most  commonly  employed  are  shown  below. 

1.  The  resistivity  is  frequently  expressed  as  the   resistance, 
in  ohms,  or  microhms,  of  a  wire  1  cm.  long  and  having  a  cross- 
section  of  1  sq.  cm.     This  has  commonly  been  called  the  centi- 
meter cube  resistivity.     This  name  frequently  gives  rise  to  false 
notions   as  to  the  relations  of  the  quantities  involved.     This 
quantity  is  better  designated  as  the  ohm  (cm.)  or  microhm  (cm.) 
resistivity,   which  terms  are  descriptive  of  the  units  involved. 
If  it  be  represented  by  SA,  then  a  wire  L  cm.  long  and  A  sq.  cm. 
in  section  will  have  a  resistance 

R  =  %-.  (28) 

2.  Another  unit  in  common  use  is  the  resistance  in  ohms  of  a 
wire  1  ft.  long  and  1  mil  or  0.001  in.  in  diameter.     This  is  com- 
monly called  the  foot-mil  resistivity.     It  should,  however,  be 
designated  as  the  ohms  (mil,  foot)  resistivity.     If  it  be  repre- 
sented by  SD,  then  for  circular  wires,  if  the  length  L  be  expressed 
in  feet  and  the  diameter  D  in  mils, 

*  =  %£•  (29) 

3.  The  third  method  of  expressing  resistivity  is  in  terms  of  the 
resistance  in  ohms  of  a  wire  of  uniform  cross-section,  1  m.  long 
and  1  gm.  in  mass.     This  has  commonly  been  called  the  meter- 
gram  resistivity.     The  designation  ohm  (meter,  gram)  resistivity 


228  ELECTRICAL  MEASUREMENTS 

should,  however,  be  used.  If  this  quantity  be  represented  by 
SM,  then  when  the  length  L  is  expressed  in  meters  and  the  mass 
M  in  grams, 

R  =  Sf-  (30) 

SA  and  SD  are  frequently  referred  to  as  the  "  length-section "  or 
" volume"  resistivities,  and  SM  as  the  " length-mass  resistivity" 
or  the  "mass  resistivity." 

The  relation  of  SA  to  SM  involves  the  density,  d;  for,  expressing 
SM  in  ohms, 

SM  =     Mf__  =  10,OOOflALcm.rf  '  ^ 

L>  meters  Li  cm. 

A  careful  study  by  the  Bureau  of  Standards12  of  all  available 
data  gives  for  the  density  of  commercial  copper  having  a  con- 
ductivity of  over  94  per  cent.,  8.89  at  20°C.  The  limits  of  varia- 
tion, neglecting  extreme  values,  were  found  to  be  8.87  and  8.91. 
The  density  of  annealed  and  hard-drawn  copper  is  sensibly  the 
same. 

To  find  SA,  SDt  or  SM,  the  resistance  of  the  sample,  E,  must  be 
determined  at  some  standard  temperature,  and  the  necessary 
mechanical  measurements  made  in  the  units  above  stated.  To 
determine  with  accuracy  the  section  of  a  wire  of  supposed  uniform 
cross-section  from  measurements  of  its  diameter  is  a  very  difficult 
matter  and  laborious  of  execution,  for  a  great  many  observations 
must  be  taken  by  means  of  the  micrometer  caliper,  and  even 
then  the  result  is  likely  to  be  seriously  in  error,  since  the 
square  of  the  diameter  enters  the  formula.  An  error  of  1  per 
cent,  in  the  diameter  means  2  per  cent,  in  the  area.  For  this 
reason  diameter  measurements  should  be  used  only  when  the  wire 
is  large.  In  case  the  cross-section  of  the  sample  is  uniform  but  ; 
irregular  in  outline,  such  measurements  are  of  course  impossible. 
If  the  wire  be  small,  its  average  area  or  average  diameter  is  best 
determined  by  weighing  a  known  length  of  it  in  air  and  then  in 
water,  thus  finding  the  mass  of  the  displaced  water  and  conse- 
quently the  volume  of  the  wire.  This,  however,  requires  that 
all  the  precautions  taken  in  an  exact  specific  gravity  determina- 
tion be  observed. 

The  determination  of  SM,  or  the  length-mass  resistivity,  presents 


THE  MEASUREMENT  OF  RESISTANCE         229 

the  least  experimental  difficulty,  as  the  mechanical  measurements 
are  simply  the  determination  of  a  length  and  a  weight,  both  of 
which  can  be  very  accurately  made;  consequently  the  ohm 
(meter,  gram)  resistivity  is  very  commonly  employed,  and  is 
recommended  in  preference  to  the  "length-section"  or  "volume" 
resistivities  denoted  above  by  SA  and  SD. 

The  standard  temperature  at  which  results  are  expressed  should 
not  differ  greatly  from  the  ordinary  average  atmospheric  tem- 
perature; therefore  20°C.  is  to  be  taken. 

The  electrical  qualities  of  copper  are  frequently  stated  in  terms 
of  the  conductivity,  which  is  the  reciprocal  of  the  resistivity, 
and  in  business  transactions  guarantees  are  given  as  to  per  cent 
conductivity.  In  order  that  such  guarantees  may  possess  defi- 
niteness,  some  standard  must  be  adopted.  Obviously,  the 
conductivity  of  pure  copper  would  be  the  most  proper  standard, 
but  this  is  unknown.  So  for  the  greatest  convenience  some 
reasonable  figure  must  be  agreed  upon.  What  this  figure  may 
be  is  not  of  consequence,  but  that  it  should  be  universally 
recognized  is  of  the  greatest  moment. 

Many  different  standard  values  of  the  resistivity  of  annealed 
copper  have  been  in  use  and  sanctioned  by  various  electrotech- 
nical  societies.  Generally  these  values  have  been  based  on  the 
work  of  Matthiessen  on  supposedly  pure  copper  (1862),  but  the 
results  on  annealed  copper  involve  an  assumption  as  to  the  ratio 
of  the  resistivity  of  the  hard-drawn  to  the  annealed  wire.  There 
are  also  uncertainties  as  to  the  temperature  coefficients,  the  many 
digits  usually  given  in  the  constants  being  without  significance; 
consequently  the  values  derived  by  various  persons  from  Mat- 
thiessen's  work  do  not  agree,  and  the  so-called  Matthiessen 
standard  has  had  no  universal  significance. 

To  obviate  this  difficulty  the  Bureau  of  Standards,  at  the 
request  of  the  American  Institute  of  Electrical  Engineers,  has 
investigated  the  subject,  and  as  the  result  of  measurements 
upon  89  samples  of  commercial  copper,  procured  from  14  differ- 
ent refiners,  an  average  result  of  0.15292  ohm  (meter,  gram) 
at  20° C.  was  obtained.  This  value  is  seen  to  be  in  close  agree- 
ment with  the  figure  0.15302  ohm  (meter,  gram)  at  20°,  which 
had  previously  been  adopted  by  the  Bureau.  This  latter  figure 
was  suggested  for  international  adoption,  but  the  German 


230  ELECTRICAL  MEASUREMENTS 


engineers  had  already  in  use  a  standard  of  conductivity,  58 

(meter,  mm.2)  at  20°,  which  is  slightly  different  from  the  above. 
The  corresponding  figure  for  the  resistivity  was  the  one  finally 
recommended  for  adoption  in  America  and  Germany,  with  a 
likelihood  of  its  immediate  adoption  in  other  countries.  It  is: 

INTERNATIONAL  ANNEALED  COPPER  STANDARD 

Mass  resistivity  .....       0.  15328  ohm  (meter,  gram)  at  20°C. 

875.20  ohms  (mil,  pound)  at  20°C. 
Volume  resistivity.  .  .        1.7241  microhm  (cm.)  at  20°C. 

0.017241  ohm  (meter,  mm.2)  at  20°C. 
0  .  67879  michrom  (inch)  at  20°C. 
10.371  ohms  (mil,  foot)  at  20°C. 
Density    (grams    per 
cubic  cm.)  .........         8  .  89  at  20°C. 

Resistivity-temperature  Constant.  —  The  changes  in  the  re- 
sistivity of  copper  due  to  alterations  of  temperature  are  com- 
plicated by  the  expansion  of  the  material.  This  effect  is  very 
small  and  is  readily  allowed  for. 

Assuming  that  the  resistance  is  measured  between  terminals 
rigidly  attached  to  the  specimen,  in  general  for  the  ohm  (meter, 
gram)  resistivity, 

MR 


Introducing  the  temperatures  and  denoting  the  coefficient  of 
linear  expansion  by  7, 

+  a™[t  -  20]) 

+  y[t  -  20])2   ' 


For  copper,  7  is  a  very  small  quantity,  0.000017,  and  so 

[SM]t  =  [SM]zo{l  +  feo  -  2y)[t  -  20]}  approximately. 
For  standard  copper,  100  per  cent,  conductivity, 

[SM]t  =  0.15328(1  +  (0.00393  -  0.000034)[£  -  20]}  ; 
=  0.15328  +  0.000597[£  -  20]. 

The  change  per  degree  in  the  resistivity  is  seen  to  be  0.000597  ohm; 
this  figure  is  independent  of  the  temperature  of  reference,  and 
in  consequence  of  (25)  applies  to  coppers  of  all  conductivities.  It 
is  called  the  (<  resistivity-temperature  constant." 


THE  MEASUREMENT  OF  RESISTANCE         231 

If  the  effects  of  expansion  had  been  neglected,  the  result  would 
have  been  0.000602. 

Using  the  volume  resistivity,  in  general, 

RA 

SA    =:    -£- 

At  t° 

r  „  ,         flaoAaoCl  +  a2o[*-20l)(l+ 
L20(l  +  7[*  -  20]) 


=  [&j2ol  +  (020  +  T)[£  —  20]     approximately. 
Using  microhms, 

[SJi  =  1.7241(1  +  (0.00393  +  0.000017)[£  -  20]}  ; 
=  1.7241  +  0.00681[£  -  20]. 

In  this  case  the  "  resistivity-temperature  constant"  is  0.00681. 
Again,  using  the  ohm  (mil,  foot)  resistivity, 

[SD]t  =  10.371  +  0.0409[^  -  20]. 

Here  the  "  resistivity-temperature  constant"  is  0.0409. 

Relation  Between  Resistivity  and  the  Temperature  Coefficient  of 
Resistance.  —  As  shown  above,  the  change  in  the  ohm  (meter,  gram) 
resistivity  per  degree  C.  is  0.000597;  consequently,  the  temperature 

coefficient  of  the  ohm  (meter,  gram)  resistivity  =  -  W""!  ---- 

[^M\tl 

The  resistance  of  a  wire  at  t°,  if  ti  is  the  temperature  of 
reference,  is  given  by 


=  Rt  \  1  +  (0-r0^)0|97  +  0.000034)  (t  -  t,)  }  approx. 

V        & 


i 

For  the  copper  met  with  in  practice  this  is  approximately 

|         0.000602  1 

*«"*,i1      "1537  ^"'w  J 

.'.  the  temperature  coefficient  of  resistance  at  the  reference 

_    .    0.000602 
temperature  t  i  is  —  r«-  ,  -- 


232  ELECTRICAL  MEASUREMENTS 

Similarly  for  SA, 

0.00678 
at   =  -vq--,  — 

i»4«i 

For  SD  it  is 

_  0.0407 

at,  ~    re  i     ' 
l&iw, 

Per  Cent.  Conductivity.  —  The  per  cent,  conductivity  is  ob- 
tained by  dividing  the  resistivity  of  the  annealed  copper  stand- 
ard at  20°  by  that  of  the  sample  at  20°. 

It  is  to  be  noticed  that  on  account  of  the  relation  of  the  tem- 
perature coefficient  to  the  conductivity,  the  per  cent,  conductivity 
of  a  sample  when  referred  to  the  standard  copper  will  depend 
somewhat  on  the  temperature  at  which  the  conductivity  is 
computed.  For  instance,  if  copper  of  resistivity  0.15328  ohm 
(meter,  gram)  at  20°  be  taken  as  a  standard,  the  resistivity  at 
0°  will  be  0.15328  -  0.000597  X  20  =  0.14134;  a  copper  which 
has  95  per  cent,  conductivity  at  20°  will  have  a  resistivity  of 
0.16134,  and  at  zero  a  resistivity  of  0.16134  --  0.000597  X 
20  =  0.14940.  Therefore  the  per  cent,  conductivity  at  0°  is 

0  14134 

100  =  94.6  per  cent. 


To  avoid  possible  confusion,  per  cent,  conductivities  are  to  be 
computed  at  20°C. 

Resistivity  of  Aluminum.  —  The  Aluminum  Co.  of  America 
furnishes  the  following  data  concerning  the  resistivity  of  their 
commercial  product  of  hard-drawn  aluminum. 

Mass  resistivity  .....     0.0764  ohm  (meter,  gram)  at  20°C. 
436.0         ohm  (mils,  pound)  at  20°C. 

Volume  resistivity.  .  .     2.828    microhm  (centimeter)  at  20°C. 
1.113    microhm  (inch.)  at  20°G.. 

Density,  grams  per  cubic  cm.  2.70. 
Mass  per  cent,  conductivity  200.7%. 
Volume  per  cent,  conductivity  61.0%. 

Conductivity  Bridges.  —  In  wire  works  and  in  the  testing 
laboratories  of  large  consumers  of  wire,  it  is  necessary  to  have 
special  apparatus  for  the  determination  of  conductivity,  the 
requirements  being  : 


THE  MEASUREMENT  OF  RESISTANCE         233 

1.  Convenience  of  manipulation;  allowing  speed  to  be  attained. 

2.  No  calculation  required;  that  is,  the  instrument  must  be 
direct  reading  in  terms  of  the  accepted  standard  material. 

3.  Freedom  from  all  temperature  corrections. 

4.  Accuracy  to  % o  or  Mo  Per  cent. 

One  form  of  such  an  apparatus  is  the  Hoopes  conductivity 
bridge.  This  device  is  an  adaptation  of  the  Kelvin  double 
bridge,  the  scheme  being  as  follows: 

Excess  of  Weight  Scale 


N 


Slide  ct    Wire 
i. 

i & 

Slide    f    Wire 


FIG.  128. — -Hoopes  conductivity  bridge. 

Hoopes  Conductivity  Bridge. — The  standard  P  and  the  un- 
known X  are  of  the  same  metal;  consequently  if  care  be  taken 
that  they  are  at  the  same  temperature,  all  corrections  due  to  tem- 
perature are  avoided.  The  arms  M,  N,  m}  n  are  in  the  same 
case  and  made  of  material  of  low  temperature  coefficient,  so 
that  their  relative  values  will  not  change.  The  sliders  c,  d,  are 

M 
rigidly  connected  so  that  when  they  are  moved  the  ratio  •«•  is 

altered  while  the  relation  -^r=  —  is  maintained. 

N        n 


234  ,       ELECTRICAL  MEASUREMENTS 

The  sample  shown  at  X  is  placed  alongside  a  scale  divided  into 
100  equal  parts;  the  graduations  therefore  represent  percentages 
of  the  total  length  of  the  scale. 

Consider  X  to  be  of  uniform  cross-section  and  100  per  cent, 
conductivity,  that  a  and  b  are  set  at  0  and  100,  respectively,  and 
that  the  resistance  of  P  equals  that  of  X;  for  balance  c  and  d 
must  be  set  so  that  M  =  N.  Now  suppose  that  the  sample  at  X 
is  changed  for  one  of  the  same  diameter,  but  of  50  per  cent,  con- 
ductivity; the  length  required  to  balance  P,  contacts  c  and  d 
remaining  fixed,  will  be  only  50  per  cent,  as  great  as  in  the  first 
case,  and  b  must  be  moved  along  the  percentage  scale  to  the 
50  per  cent.  mark. 

However,  the  samples  X  vary  in  diameter,  while  the  resistance 

M 
of  P  is  fixed;  consequently  the  ratio  ^-  must  be  variable,  so 

that  it  may  be  made  to  correct  for  the  cross-section  of  the  sample. 
To  obtain  the  relative  diameters  of  wires  it  is  more  accurate  and 
convenient  to  weigh  samples  of  the  same  length  than  to  caliper 
them;  accordingly,  all  samples  are  cut  to  a  length  of  38  in.  in  a 
special  machine  and  weighed.  The  contact  c  is  then  set  at  the 
graduation  corresponding  to  the  excess  or  defect  in  the  weight, 

M 
referred  to  a  sample  of  correct  size,  thus  making  ^-  P  equal  to 

the  resistance  of  a  sample  of  100  per  cent,  conductivity — length 
0-100  on  the  percentage  scale — and  of  the  same  diameter  as 
X.  The  bridge  is  then  balanced  by  moving  b,  and  the  con- 
ductivity is  read  from  the  scale. 

Several  standards  are  provided;  they  are  removable,  and  by 
the  use  of  the  taps  e,  f,  g,  each  has  a  range  of  three  consecutive 
numbers  on  the  B.  &  S.  gage.  For  rapid  work  the  stock  of 
samples  must  be  kept  at  the  temperature  of  the  testing 
apparatus. 

The  coarse  adjustment  of  the  slider  b  is  effected  by  the  handle 
projecting  toward  the  front  of  the  bridge;  the  final  balancing  is 
made  by  turning  the  milled  head  at  the  front. 

The  percentage  scale  is  seen  at  the  back  of  the  instrument,  the 
excess  of  weight  scale  at  the  right  hand. 

The  instrument  is  covered  by  a  metal-lined  wooden  case,  which 
serves  to  keep  the  temperature  constant;  the  reading  is  made 


THE  MEASUREMENT  OF  RESISTANCE         235 

through  a  glazed  window  in  the  top.     Provision  is  made  in  the 
case  for  storing  the  samples  to  be  tested. 

References 

1.  "  Note  on  the  Use  of  the  Differential  Galvanometer,"  C.  W.  S.  CRAW- 
LEY,  Journal  Institution  Electrical  Engineers,  vol.  30,  1901,  p.  908. 

2.  "Zur  Anwendung  des  Differential  galvanometers  bei  genauen  Wider- 
standsmessungen,"  W.  JAEGER,  Zeit.  fur  Instrumentenkunde,  vol.  24,  1904, 
p.  288. 

3.  "Ueber      eine      Stopselanordnurg     fiir      Briickenzweigwiderstande," 
O.  SCHONE,  Zeit.  fur  Instrumentenkunde,  vol.  18,  1898,  p.  133. 

4.  "On  the  Measurement  of  Resistance,"  ARTHUR  SCHUSTER,  Phil.  Mag., 
vol.  39,  1895,  p.  175.     "On  Methods  of  High  Precision  for  the  Comparison  of 
Resistances,"  F.  E.  SMITH,  Report,  British  Association  for  the  Advancement 
of  Science,  1906,  p.  106.     "On  Methods  of  High  Precision  for  the  Comparison 
of    High    Resistances,"  F.  E.  SMITH,    The   Electrician,  vol.    57,  1906,  pp. 
976-1009. 

5.  "On  Bridge  Methods  for  Resistance  Measurements  of  High  Precision 
in  Platinum  Thermometry,"  F.  E.  SMITH,  Phil.  Mag.  vol.  24,  1912,  p.  541. 
Collected  Researches,  Nat.  Phys.  Lab.,  vol.  9,  1913,  p.  221. 

6.  "Prazisionsmessungen  an  kleinen  Widerstanden  in  der  Thomsoncher 
Briicke,    W.   JAEGER,    ST.   LINDECK,    H.    DIESSELHORST,    Zeit.  fur  Instru- 
mentenkunde, vol.  23,  1903,  pp.  33  and  65. 

7.  "Adjustments  of  the  Thomson  Bridge  in  the  Measurement  of  Very 
Low  Resistances,"  F.  WENNER  and  E.  WEIBEL,  Bulletin  of  the   Bureau  of 
Standards,  vol.  11,  1914,  p.  65.     Scientific  Papers  of  the  Bureau  of  Stand- 
ards,   No.    225.     "The    Four    Terminal    Conductor  and    the    Thomson 
Bridge,"  FRANK  WENNER,  Bulletin,  Bureau  of  Standards,  vol.  8, 1912,  p.  559. 

8.  "  Precision  Resistance  Measurements  with  Simple  Apparatus,"  E.  H. 
RAYNER,  Proc.  Physical  Society  of  London,  vol.  27,  1915,  p.  385. 

9.  "On  the  Determination  of  the  Insulation  Resistance  of  Faults  During 
Working,"  O.  FROELICH,  The  Electrician,  vol.  30,  1893,  p.  475. 

10.  "  Measurement  of  Insulation  Resistance  and  Capacity  of  Individual 
Conductors    of    an    Alternating-current     Network    During    Working,"   J. 
SAHULKA,  The  Electrician,  vol.  59,  1907,  p.  999. 

11.  "Measurement  of  the  Insulation  Resistance  of  an  Electric  Wiring  Sys- 
tem," E.  F.  NORTHRUP,  Electrical  World,  vol.  43,  1904,  p.  966. 

12.  Copper  Wire  Tables,  third  edition,  Circular  No.  31,  Bureau  of  Stand- 
ards, 1914.     "The  Electrical  Conductivity  of  Copper,"  F.  A.  WOLFF  and 
J.  H.   DELLINGER,  Bulletin,   Bureau  of  Standards,   vol.   7,   1911,  p.    103. 
"The  Temperature  Coefficient  of  Resistance  of  Copper,"  J.  H.  DELLINGER, 
Bulletin,  Bureau  of  Standards,  vol.  7,  1911,  p.  71. 

13.  "The    Measurement    of    High    Temperature,"    BURGESS  and    LE 
CH ATELIER,  John  Wiley  and  Sons,  1912.       "  Platinum  Resistance  Thermo- 
metry  at    High   Temperatures,"   C.   W.   WAIDNER  and  G.  K.  BURGESS, 
Bulletin,  Bureau  of  Standards,  vol.  6,  1909-10,  p.  149. 


CHAPTER  V 


THE  MEASUREMENT  OF  POTENTIAL  DIFFERENCE 
AND  ELECTROMOTIVE  FORCE 

The  most  obvious  method  of  determining  the  potential  differ- 
ence between  two  points  in  a  circuit  is  to  connect  them  through 
a  suitable  galvanometer  which  is  in  series  with  a  high  resistance. 
The  potential  difference,  P.D.,  is  the  product  of  the  galvanometer 
current  and  the  total  resistance  of  the  galvanometer  circuit. 
The  galvanometer  and  the  resistance  may  be  combined  in  a 


FIG.   129. — WeSton  moving-coil  voltmeter  for  direct-current  circuit. 

single  instrument  and  such  " potential  galvanometers"  were  in 
common  use  before  the  introduction  of  voltmeters  or  instru- 
ments where  the  products  are  taken  once  for  all  and  marked 
on  the  scales.  The  various  types  of  instruments  which  have 
been  described  as  ammeters  may  be  used  as  voltmeters,  provided 
the  total  resistance  of  the  instrument  be  made  sufficiently  high 
by  the  use  of  proper  windings  and  series  resistances.  There  are 
differences  of  detail;  for  example,  the  resistance  of  the  controlling 

236 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    237 

springs  need  not  be  kept  as  low  as  in  ammeters.  For  direct- 
current  work,  the  moving-coil  type  of  instrument  has  become  the 
standard;  for  alternating  currents,  the  electrodynamometer 
type  is  usual,  though  there  are  some  soft  iron  and  induction 
instruments. 

In  direct-current  voltmeters  the  resistance  is  about  100  ohms 
per  volt  of  full  scale  reading ;  the  resistance  of  alternating-current 
voltmeters  of  the  electrodynamometer  type  is  much  lower,  about 
20  ohms  per  volt.  It  is  customary  to  make  the  final  adjustment 
of  the  instruments  by  altering  the  series  resistance,  but  it  is  more 
convenient,  when  multipliers  are  to  be  used,  to  have  a  definite 
resistance  per  volt  and  to  effect  the  adjustment  in  some  other 
manner. 

In  direct-current  portable  instruments  having  ranges  up  to 
about  750  volts,  it  is  usual  to  place  the  series  resistance  within 
the  base.  Self-contained  alternating-current  portable  voltmeters 
having  a  range  of  300  volts  may  be  obtained. 

When  using  a  voltmeter,  it  should  be  kept  in  mind  that  it  only 
shows  the  P.D.  between  its  own  terminals  and  that  this  is  not 
necessarily  the  same  as  the  P.D.  which  previously  existed  between 
the  points  on  the  circuit  to  which  the  terminals  are  applied. 
For  example,  suppose  there  is  a  large  resistance,  32,000  ohms, 
across  which  the  drop  is  200  volts  and  that  it  is  desired  to  measure 
the  P.D.  between  one  terminal  and  a  tap  at  the  middle  of  th& 
resistance.  Obviously,  the  P.D.  in  question  is  100  volts;  however, 
if  a  voltmeter  of  16,000  ohms  resistance  is  applied  between  one 
terminal  and  the  tap,  it  will  read  66.6  volts.  The  application 
of  the  voltmeter  has  changed  the  quantity  which  it  is  desired  to 
measure  by  33  per  cent.  The  disturbance  of  the  circuit  condi- 
tions diminishes  as  the  resistance  of  the  voltmeter  is  increased 
and  would  be  nil  with  an  instrument  which  operated  on  open 
circuit,  that  is,  an  electrostatic  voltmeter.  In  engineering  work 
this  difficulty  is  not  often  met  but  one  should  not  lose  sight  of 
the  possibility. 

Effect  of  Temperature. — It  is  evident  that  a  high  resistance, 
which  must  not  be  subject  to  changes  due  to  the  heating  action 
of  the  current  or  to  alterations  of  room  temperature,  is  an 
essential  part  of  any  electromagnetic  voltmeter.  As  the 
instrumental  errors  should  be  practically  independent  of  tern- 


238 


ELECTRICAL  MEASUREMENTS 


perature,  the  major  portion  of  the  resistance  must  be  of  a 
material  having  a  negligible  temperature  coefficient.  In  addi- 
tion, the  effect  of  temperature  on  the  controlling  springs,  and  in 
direct-current  instruments  the  effect  on  the  magnets,  must  be 
small.  The  springs  grow  weaker  by  about  0.04  per  cent,  per 
degree  C.  as  the  temperature  is  raised.  Usually  the  magnets 
grow  weaker  with  an  elevation  of  temperature,  an  average  value 
for  the  temperature  coefficient  being  —0.025  per  cent,  per  degree 
C.  The  net  effect  of  temperature  on  a  150-volt  direct-current 
portable  voltmeter  of  good  design  is  about  +  0.012  per  cent, 
per  degree. 


FIG.  130. — Multipliers  for  extending  the  range  of  voltmeters  and  wattmeters. 


The  effect  of  temperature  variation  becomes  more  important 
when  low-range  instruments  are  used  for  in  them  the  movable  coil, 
which  is  always  wound  with  copper  wire,  forms  a  relatively  larger 
proportion  of  the  total  resistance. 

Multipliers. — Frequently  it  is  necessary  to  measure  potential 
differences  higher  than  those  for  which  the  voltmeter  was  origi- 
nally intended.  In  this  case  a  properly  constructed  resistance 
is  joined  in  series  with  the  instrument  so  that  the  voltage 
necessary  to  force  a  given  current  through  the  voltmeter  circuit 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    239 

is  increased;  then  if  RM  and  Rv  be  the  resistances  of  the  multiplier 
and  of  the  voltmeter  respectively, 

P.D.  =  reading  times  (Rv  +  R» 


When  the  range  is  very  greatly  extended,  to  several  thousand 
volts,  the  multiplier  is  subdivided  and  mounted  in  a  number  of 
boxes,  thus  reducing  the  voltage  drop  between  neighboring  wires 
and  rendering  it  easier  to  insulate  them.  Also,  capacity  effects 
which  might  be  serious  in  alternating-current  work  are  much 
reduced,  for  high-range  multipliers  may  be  subject  to  errors  due 
to  distributed  capacity  and  capacity  to  ground. 

The  condensation  of  moisture  on  the  resistors  of  very  high- 
range  multipliers,  when  they  are  used  in  air,  frequently  gives 
rise  to  burnouts.  These  may  be  obviated  by  immersing  the 
multiplier  in  transformer  oil.  Multipliers  often  contain  soft 
rubber  insulation,  this  must  be  removed  before  the  immersion. 

Electrodynamometer  Voltmeters.  —  These  instruments  are 
primarily  designed  for  the  measurement  of  alternating  potential 
differences.  The  indicating  portion  is  a  comparatively  delicate 
electrodynamometer  with  a  pivoted  movable  coil. 

The  current  through  an  alternating  current  voltmeter  is  given  by 


7_ 

" 

where  R  and  L  are  respectively  the  total  resistance  and  inductance 
of  the  voltmeter  and  w  is  2ir/.  At  the  ordinary  commercial 
frequencies,  the  indications  must  be  practically  independent  of 
the  frequency  but  as  L  can  never  be  zero,  the  resistance 
must  be  made  so  high  that  the  reactance  can  be  neglected 
in  comparison  with  it.  The  instrument  may  then  be  used  for 
both  direct  and  alternating  potential  differences.  This  is  a 
convenience,  for  it  may  then  be  calibrated  with  direct  cur- 
rents, using  reversals. 

As  the  electrodynamometer  is  a  comparatively  insensitive  in- 
strument, considerable  current  is  required  and  it  is  not  possible, 
while  retaining  the  characteristics  of  portability  and  solidity 
of  construction  necessary  in  order  that  the  instrument  may  have  a 
long  life  and  maintain  its  accuracy  under  the  trying  conditions 
of  everyday  work,  to  give  this  form  of  voltmeter  as  high  a  re- 


240 


ELECTRICAL  MEASUREMENTS 


sistance  as  is  common  in  direct-current  instruments.  This  is  a 
disadvantage,  for  it  increases  the  liability  of  altering  the  circuit 
conditions  by  the  application  of  the  instrument.  The  resistance 
of  a  150-volt  instrument  of  this  type  is  from  2,500  to  3,000  ohms. 
Low  ranges  are  obtained  by  reducing  the  series  resistance,  and 

as  the  inductance  remains  the 
same,  the  likelihood  of  a  fre- 
quency error  is  much  increased. 
In  investigation  work  it  is 
sometimes  necessary  to  measure 
voltages  on  circuits  of  abnor- 
mally high  frequency,  500  to 
1,000  cycles  per  second.  In  this 
case,  if  a  dynamometer  volt- 
meter is  used,  the  inductance 
term  will  not  be  negligible.  Its 
value  will  depend  on  the  posi- 
tion of  the  movable  coil.  Eddy 
currents  in  the  metal  frames  as 
well  as  capacity  effects  between 
the  coils  and  in  the  series  resis- 
tance also  modify  the  action  of 
the  instrument. 


FIG.  131.— Shielded  dynamometer  voltmeter,  General  Electric  Co. 

A  certain  alternating-current  voltmeter  of  the  electrody- 
namometer  type  had  a  resistance,  when  measured  with  direct 
current,  of  1,557  ohms.  This  agreed  with  the  resistance  meas- 
ured with  an  alternating  current  of  16  cycles  per  second.  The 
effective  inductance  at  16  cycles  per  second  (and  110  volts 
deflection)  was  0.061  henry.  At  3,000  cycles  per  second  the 
effective  resistance  was  1,675  ohms  while  the  effective  inductance 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    241 

was  0.053  henry.  While  there  was  no  appreciable  error  at  16 
cycles  per  second,  the  error  in  the  indication  at  3,000  cycles  per 
second  was  25+  per  cent. 

Fig.  131  shows  the  general  construction  of  a  dynamometer 
voltmeter.  The  working  parts  of  the  instrument  are  surrounded 
by  a  laminated  magnetic  shield.  Electromagnetic  damping  is 
obtained  by  having  the  movable  system  carry  a  fan-shaped 
sector  of  aluminum,  which  swings  between  the  poles  of  two  small 
permanent  magnets.  The  shielded  voltmeter  made  by  the  Wes- 
ton  Instrument  Co.  is  very  similar  in  general  design  to  the 
wattmeter  shown  in  Fig.  177;  it  has  a  very  efficient  air  damper, 
consisting  of  two  light,  symmetrically  disposed  vanes  which  are 
enclosed  in  carefully  finished  chambers  in  the  base  of  the  frame- 
work which  supports  the  coils.  The  vanes  are  of  exceedingly 
thin  metal  stiffened  by  ribs  stamped  into  them  and  by  the  edges 
which  are  turned  over.  The  useless  leakage  to  the  outside  air 
is  reduced  to  a  minimum  and  the  desired  degree  of  damping 
attained  by  a  suitably  designed  clearance  space  between  the 
vanes  ^and  the  walls  of  the  chamber  (see  page  71).  The  mo- 
ment of  inertia  of  the  moving  parts  of  this  arrangement  is  very 
small. 

Hot-wire  Voltmeters. — The  first  instrument  particularly 
adapted  to  the  measurement  of  alternating  potential  differences 
was  the  Cardew  voltmeter,  invented  by  Major  Cardew,  R.  E. 

In  this  instrument  the  current  was  passed  through  a  long  thin 
wire  of  platinum-silver,  and  by  a  suitable  mechanism  the  ex- 
pansion of  this  wire,  due  to  its  rise  of  temperature,  caused  the 
index  to  move  over  the  scale.  Later  designers  have  been  able 
to  improve  on  Cardew's  arrangement  for  translating  the  ex- 
pansion of  the  wire  into  the  movement  of  the  index,  so  that  a 
much  shorter  wire  may  be  employed,  thus  rendering  the  in- 
strument less  cumbersome. 

The  ingenious  multiplying  device  used  by  Hartmann  and 
Braun  is  shown  in  principle  in  Fig.  132. 

The  active  wire  ADB  is  of  platinum-iridium,  DEC  is  a  very 
fine  phosphor-bronze  wire,  and  EFG  is  a  silk  fiber  which  passes 
once  around  the  drum  F  and  is  drawn  taut  by  the  spring  S.  On 
the  passage  of  the  current,  ADB  is  heated  and  expands,  the 
slack  is  taken  up  by  the  spring  S  and  the  index  is  thus  moved 

10 


242 


ELECTRICAL  MEASUREMENTS 


over  the  scale.  The  vane  W  moving  in  the  air  gap  of  the  per- 
manent magnet  M  serves  as  a  damping  device.  The  moving 
system  is  carried  by  insulating  studs  at  A,  B  and  C.  These  are 


FIG.  132. — Diagram  for  Hartmann  &  Braun  hot-wire  voltmeter. 

supported  on  a  back  plate  constructed  of  two  metals  in  such  a 
proportion  that  the  net  coefficient  of  expansion  is  the  same  as 
that  of  the  wire,  so  the  effect  of  changes  of  room  temperature  is 
minimized.  The  position  of  the  end  A  of  the  working  wire  may 

be  altered  by  turning  the  screw  V  and 
the  zero  position  of  the  pointer  thus 
adjusted.  The  coefficient  of  expansion 
of  the  platinum-iridium  wire  is  less 
than  that  of  the  platinum-silver  wire 
formerly  used;  it  can  be  run,  however, 
at  a  much  higher  temperature,  the  re- 
sult being  a  considerable  reduction  of 
the  zero  shift,  which  is  troublesome  in 
hot-wire  instruments. 

The  working  parts  of  the  Roller  hot- 
wire voltmeter  are  sketched  in  Fig.  133. 
The  pivot  D  carries  a  pulley  B  and  the 
forked  arm  DFG.  A  silk  fiber  is 
stretched  between  F  and  G.  This 

1  passes  around  and  is  made  fast  to  the 

FIG.     133. — Diagram    for      .  ,    ,  w    ,         ,  .  ,     ,,  .    , 

Roller  hot-wire  voltmeter.     Pivoted  drum  E,  to  which  the  pointer 

is  attached.  It  is  evident  that  any  ro- 
tation of  the  drum  D  will  cause  the  pointer  to  move  over  the 
scale.  The  wire  ABC  passes  around  and  is  made  fast  to  the 
pulley  B.  The  current  flows  through  the  wire  A  B  since  the  end 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    243 

C  is  insulated.  The  wire  is  in  tension  due  to  the  spring  S. 
Normally  the  tension  of  the  sections  AB  and  CB  is  the  same; 
on  the  passage  of  the  current,  A B  expands  and  the  equality  of 
tension  is  restored  by  the  rotation  of  B,  which  at  the  same  time 
moves  the  pointer. 

As  the  wires  AB  and  CB  are  of  the  same  material  and  mass, 
the  effect  of  variation  of  room  temperature  is  compensated,  even 
though  it  be  rapid. 

The  whole  movable  system  is  mounted  on  a  plate  which  can  be 
rotated  about  the  point  E;  the  zero  adjustment  is  thus  provided. 

In  American  practice,  hot-wire  instruments  are  not  used  on 
switchboards.  They  are  very  useful  in  the  laboratory,  for  being 
adapted  to  the  measurement  of  both  alternating  and  direct  cur- 
rents, they  can  be  used  as  transfer  instruments  in  the  calibration 
of  alternating-current  ammeters  and  voltmeters.  The  alternat- 
ing-current instrument  may  be  compared,  under  normal  condi- 
tions of  frequency  and  wave  form,  with  the  hot-wire  instrument 
and  the  latter  calibrated  immediately  by  use  of  the  direct-current 
potentiometer. 

When  instruments  of  this  type  are  first  placed  in  circuit,  enough 
time  should  be  allowed  for  them  to  come  to  their  stable  condition 
before  the  readings  are  taken. 

The  advantages  of  hot-wire  instruments  are:  they  have  no 
self-heating  errors,  are  not  influenced  by  local  fields  and  are  unin- 
fluenced by  changes  of  frequency  and  wave  form;*  the  last  is  in 
consequence  of  their  low  inductance.  Their  disadvantages  are 
that  they  are  sluggish  in  action,  the  zero  is  unstable,  they  are 
easily  burned  out  by  overloads,  and  the  resistance  of  the  voltmeter 
is  low. 

ELECTROSTATIC  INSTRUMENTS 

In  instruments  of  this  class,  advantage  is  taken  of  the  electro- 
static attraction  existing  between  bodies  charged  to  different 
potentials.  The  magnitude  of  the  force  depends  on  the  geometry 

*  In  strictness  this  remark  applies  only  to  instruments  where  the  whole 
current  is  taken  through  the  hot  wire.  There  are  certain  forms  of  instru- 
ments which  are  equivalent  to  shunted  ammeters  in  their  construction. 
They  will  show  frequency  errors  at  the  very  high  periodicities  used  in  radio- 
telegraphy*  (see  page  63). 


244 


ELECTRICAL  MEASUREMENTS 


of  the  system  of  conductors,  the  relative  potentials  of  its  parts 
and  the  dielectric  coefficient  of  the  medium  separating  the 
attracting  bodies. 

The  Attracted-disc  Electrometer. — The  first  suggestion  of  the 
attracted-di'sc  electrometer  was  due  to  Sir  William  Snow-Harris, 
who  used  an  instrument  of  this  sort.  Its  essential  members  were 
a  fixed  circular  plate  electrode  supported  by  an  insulating  stan- 
dard, and  a  movable  plate  electrode  hung  directly  over  the  fixed 
plate  from  the  arm  of  a  gravity  balance.  By  putting  weights  in 
the  scale  pan,  a  balance  could  be  secured  and  a  measure  of  the 
electrostatic  attraction  and  consequently  of  the  P.D.  between 
the  electrodes  obtained.  A  defect  of  any  such  simple  arrange- 
ment, which  renders  it  useless  as  an  ab- 
solute instrument,  is  that  owing  to  the 
influence  of  the  edges  of  the  plates  the 
distribution  of  the  charges  over  the 
surfaces  will  not  be  uniform.  This 
renders  inexact  the  application  of  a 
simple  formula  for  the  attraction  be- 
tween the  two  plates,  based  on  the 
assumption  of  a  uniform  density  of  dis- 
tribution of  the  charge. 

The  distribution  of  the  charges  over 

FIG.     134. — Elements   rof  the    central    portions    of   two    parallel 
eleC"  plates,  whose  dimensions  are  large  com- 


pared with  their  distance  apart,  will  be 
practically  uniform.  Therefore,  if  the  force  exerted  on  the  cen- 
tral portion  of  one  of  the  plates  is  measured,  the  use  of  a  for- 
mula which  assumes  a  uniform  distribution  will  be  legitimate. 

Lord  Kelvin  secured  a  practically  uniform  distribution  by  the 
use  of  the  guard  ring.  This  is  a  broad  ring  closely  surrounding, 
but  not  touching,  the  movable  member  and  in  electrical  connec- 
tion with  it.  The  stationary,  or  attracting  plate,  has  the  same 
diameter  as  the  guard  ring. 

Absolute  electrostatic  instruments  are  not  of  industrial  import- 
ance; however,  the  application  of  the  guard-ring  principle  will  be 
illustrated  by  the  Kelvin  absolute  electrometer,  the  elements  of 
which  are  shown  in  Fig.  134. 

In  this  instrument  the  attraction  on  the  movable  member  is 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    245 

weighed  by  a  calibrated  spring  balance.  The  guard  ring  and  at- 
tracted disc  are  supported  from  the  sides  of  a  large  glass  jar  which 
serves  as  a  case  for  the  instrument;  the  disc  is  made  of  aluminum 
and  is  carried  by  three  small  springs,  having  the  shape  of  coach 
springs.  These  are  supported  from  an  insulating  rod,  which  by 
the  use  of  a  micrometer  screw,  B,  can  be  raised  or  lowered  through 
known  amounts.  In  order  that  the  attracted  disc  may  always  be 
returned  to  its  proper  zero  position,  with  its  lower  surface 
coplanar  with  that  of  the  guard  ring,  a  sighting  arrangement  is 
provided.  A  fine  hair  is  stretched  between  two  small  pillars  at 
the  center  of  the  disc;  this  hair  is  at  the  focus  of  a  lens  which 
forms  an  image  between  the  points  of  two  small  screws  carried  by 
the  guard  ring.  The  image  of  the  hair  and  the  points  of  the 
screws  are  viewed  through  a  lens. 

When  the  disc  is  in  its  zero  posi-     ^ardRing  |f  /AttracIrearAte' 

tion  the  hair  appears  to  bisect     ^     ==1  c=  •       '  c=:      ^ Vz 

the  distance  between  the  points. 
The  attracted,  disc  is  shielded     c= 


from  extraneous  action  by  the    '  Attracting  Plate/ 

~       „,,  FIG.  135. — Pertaining  to  attracted- 

removable  box  C.     The  attract-  disc  electrometer. 

ing  plate  is  carried  on  an  insulat- 
ing glass  rod  D  and  can  be  moved  vertically  through  known 
amounts  by  means  of  the  micrometer  screw  E.  T  is  the  well- 
insulated  terminal  connecting  with  the  attracting  plate.  Con- 
nection between  the  guard  ring  and  the  attracted  disc  is  made  by 
a  flexible  wire. 

The  relation  between  the  difference  of  potential  of  the  plates 
and  the  force  of  attraction  may  be  established  thus: 

Referring  to  Fig.  135,  the  attracted  plate  has  an  area  of  A  sq. 
cm.  and  is  distant  S  cm.  from  the  attracting  plate.  Vz  and  Vi 
are  the  potentials  of  the  two  plates.  The  arrangement  forms  an 
electrical  condenser  and  if  S  is  small  compared  with  the  size  of  the 
plates,  the  capacity  will  be 

O  A       r>* 


The  energy  necessary  to  raise  one  plate  to  the  potential 
and  the  other  to  the  potential  V%  will  be 

"  V^  =          MS 


246  ELECTRICAL  MEASUREMENTS 

Suppose  the  upper  plate  is  given  a  small  displacement,  V\ 
and  72  being  kept  constant  by  connection  to  a  source  of  potential 
difference.  There  will  be  a  change  in  the  energy  of  the  con- 
denser which  will  be  numerically  equal  to  the  mechanical  work 
necessary  to  displace  the  plate  in  the  direction  S. 

dE  =  FdS 

^_dE        A(7!-72)2 
b    =  dS  = 


\  -  V2  =  8^ 


SirF  . 
~Am 


If  (7i  -  72)  is  in  volts,  P.D.  =  3005  J8^-  =  1,5045  J~  (3) 


It  has  been  assumed  that  all  of  the  electrostatic  lines  of  force 
are  straight  and  normal  to  the  plane  of  the  disc.  A  few  lines  will 
stray  into  the  very  narrow  gap  between  the  guard  ring  and 
the  attracted  plate.  They  may  be  assumed  to  divide  equally 
between  the  ring  and  the  plate,  so  to  make  an  approximate 
allowance,  the  effective  area  of  the  plate  may  be  taken  as  the 
area  of  the  plate  plus  one-half  the  area  of  the  air  gap. 

It  is  well  to  emphasize  the  fact  that  unless  the  voltages  are 
high,  the  forces  to  be  dealt  with  in  electrostatic  instruments  are 
small.  If 

A  =  100  sq.  cm. 

S  =  1  cm. 
P.D.  =  150  volts 
then 

F  =  1  dyne,  approximately. 

That  is,  the  force  is  about  the  same  as  the  attraction  of  gravity 
on  a  mass  of  1  mg.  To  increase  this  force,  the  plates  must  be 
brought  very  near  together,  or  the  use  of  the  instrument  re- 
stricted to  measuring  high  potentials. 

Before  using  the  absolute  electrometer,  the  spring  balance  must 
be  calibrated ;  to  do  this  the  terminals  of  the  instrument  are  short- 
circuited  and  the  disc  brought  to  its  zero  position  by  means  of 
the  micrometer  head.  Known  weights  are  then  placed  upon  the 
disc  and  the  number  of  turns  which  it  is  necessary  to  give  B  in 
order  to  return  the  disc  to  the  zero  position  is  noted.  The  number 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    247 

of  dynes  corresponding  to  one  division  of  the  micrometer  head 
can  then  be  calculated. 

The  natural  procedure  in  taking  a  measurement  would  be  first 
to  short-circuit  the  instrument  and  bring  the  attracted  disc  to 
the  zero  position  by  means  of  the  micrometer  head  B,  the  read- 
ing of  which  is  noted.  The  potential  to  be  measured  would  then 
be  inserted  between  the  terminals  of  the  instrument.  This  would 
cause  the  attracted  disc  to  move  downward.  The  disc  would 
then  be  returned  to  its  zero  position  by  turning  the  head  B,  the 
final  position  of  which  is  read.  The  difference  of  the  micrometer 
readings  gives  the  stretch  of  the  spring.  The  force  F  is  deter- 
mined from  this  stretch  and  the  calibration  of  the  spring. 

It  will  be  found  that  if  the  P.D.  is  small,  the  lower  plate 
must  be  brought  very  near  to  the  attracted  disc.  For  example, 
if  the  potential  difference  is  500  volts,  F,  100  dynes,  and  A, 
100  sq.  cm.,  the  distance  between  the  plates  will  be  only  3  mm. 
It  is  practically  impossible  to  make  and  adjust  the  plate  and  disc 
so  that  such  a  small  value  of  S  can  be  measured  with  certainty. 
Slight  irregularities  of  the  surfaces  and  lack  of  parallelism  of  the 
plates  would  vitiate  the  results. 

This  difficulty  has  been  overcome  by  Lord  Kelvin's  method  of 
using  an  auxiliary  high  potential.  Suppose  that  the  guard  ring 
and  disc  are  charged  to  a  potential  of  10,000  volts,  the  at- 
tracting plate  being  connected  to  earth.  When  the  disc  has  been 
brought  to  its  sighted  position,  corresponding  to  F  =  100, 
S  =  6.666  cm.  If  the  plate  be  now  connected  to  earth  through 
a  500-volt  battery,  thus  making  the  potential  applied  to  the 
instrument  9500  volts,  to  return  the  disc  to  its  standard  position, 
B  remaining  fixed  S  must  be  made  6.366  cm.  That  is,  the  lower 
plate  has  to  be  moved  through  a  distance  equal  to  that  which 
would  exist  between  the  plate  and  disc  if  the  P.D.  were  directly 
measured.  The  advantage  attained  is  that  in  both  measure- 
ments the  attracting  plates  are  so  far  apart  that  there  is  practi- 
cally no  uncertainty  as  to  the  value  of  S.  When  used  as  just 
suggested,  the  instrument  is  said  to  be  employed  heterostatically ; 
when  only  the  P.D.  to  be  measured  is  employed  the  electrometer 
is  said  to  be  used  idiostatically. 

The  expression  for  the  P.D.   when  the  instrument  is  used 

heterostatically    is    P.D.  =  1,504(3  -  Sf)J-      The   distance 


248 


ELECTRICAL  MEASUREMENTS 


through  which  the  attracting  plate  must  be  moved  in  order 
to  again  bring  the  cross-hair  to  its  "standard  position  after  the 
application  of  the  P.D.  to  be  measured  is  S  —  S'. 

The  glass  jar  which  forms  the  case  of  the  instrument  is  coated 
with  tin  foil  both  inside  and  outside,  and  serves  as  a  Leyden 
jar  to  hold  the  auxiliary  charge,  which  is  obtained  from  an 
electrophorus  arid  is  kept  constant  by  the  use  of  a  small 
influence  machine  called  the  replenisher.  It  will  be  noticed 
that  it  is  not  necessary  to  know  the  value  of  the  auxiliary  poten- 
tial; it  must,  however,  remain  con- 
stant throughout  the  experiment. 
To  test  this  a  small  attracted  disc 
electrometer  called  a  gage  is  pro- 
vided. As  the  electrometer  is  con- 
structed, both  the  replenisher  and 
the  gage  are  included  within  the 
case. 

The    attracted-disc    principle   is 
used  in  secondary  electrostatic  volt- 


FIG.  136. — Simple  quadrant  electrometer. 

meters  intended  for  high-tension  work  (see  page  258).  In  such 
instruments  the  guard  ring  is  omitted. 

The  Quadrant  Electrometer.— The  quadrant  electrometer, 
also  the  invention  of  Lord  Kelvin,  is  more  sensitive  and  of  much 
greater  practical  importance  than  the  absolute  instrument  just 
described.  Of  late  years  it  has  been  used  in  investigations  con- 
cerning the  energy  losses  in  dielectrics  intended  for  high-voltage 
insulations. 

The  instrument,  reduced  to  its  elements,  is  shown  in  Fig.  136, 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    249 

while  a  perfected  form,  designed  at  the  National  Physical  Labora- 
tory, and  intended  for  work  of  high  precision,  is  shown  in  Fig. 
189,  page  324. 

The  arrangement  of  conductors  is  shown  in  Fig.  136.  G,G', 
FjF'  are  the  quadrants,  usually  made  by  cutting  into  four  parts 
a  shallow  metal  box  with  its  cover;  for  low  potentials,  the 
diameter  of  the  box  is  about  3  in.,  the  depth  about  Y^  in.  The 
quadrants  are  supported  on  insulating  standards  and  are  cross- 
connected  electrically  by  the  wires  b  and  e. 

The  needle  N,  made  of  thin  aluminum  and  of  the  form  in- 
dicated, is  suspended  within  the  box  equally  distant  from  the 
top  and  the  bottom. 

The  directive  moment  is  usually  obtained  by  a  torsion  wire 
or  by  a  bifilar  suspension. 

To  deduce  the  formula  for  this  electrometer,  it  will  be  as-_ 
sumed  that  as  the  needle  deflects,  the  rates  of  variation  of  the 
capacities  of  the  condensers  formed  by  the  needle  and  the 
quadrants  are  uniform  and  independent  of  the  angular  dis- 
placement of  the  needle,  that  the  radial  cuts  dividing  the  quad- 
rants are  of  negligible  'width  and  that  only  the  five  conductors, 
F,  F',  G,  G',  N  need  be  considered. 

The  distribution  of  potentials  will  be  assumed  as  indicated 
in  Fig.  136.  Starting  from  the  point  a  the  fall  of  potential 
to  the  second  set  of  quadrants  isd  units.  The  further  fall  from 
the  second  set  of  quadrants  to  the  needle  is  V  units. 

The  needle  N  and  the  quadrants  G,  G'  form  a  condenser  which 
is  charged  by  a  potential  difference,  V,  while  the  needle  and  F, 
F'  form  a  condenser  charged  by  a  potential  (V  +  d).  The  total 
area  of  the  needle  under  G  and  G'  is  A. 

The  energy  of  the  condenser,  considering  both  sides  of  the 
needle,  is 


E  -  y2CV*  =  (4) 


L   i    (7-2^.  2\0 

l)     F2  (5) 


47T/S 

If  the  needle  be  given  a  slight  angular  displacement,  V  being 


250  ELECTRICAL  MEASUREMENTS 

kept  constant,  a  small  amount  of  work  will  be  done  which  is 
numerically  equal  to  the  change  of  electrical  energy.  If  M  is 
the  moment  causing  the  displacement  of  the  needle,  then  as 

dE 


Similarly  MF  =  (V  +  d)2- 

The  net  turning  moment  acting  on  the  needle  will  be 

M  = 


This  moment  is  balanced  by  the  torsion  of  the  suspension,  so 
if  D  is  the  deflection  and  r  the  torsion  constant 


Tt 

rD  =  '—£-a—[2Vd  +  d2]   in  absolute  electrostatic  units.      (6) 
If  volts  are  used, 


The  quadrant  electrometer  is  always  used  as  a  secondary  in- 
strument, but  the  formula  (7)  is  useful  as  an  aid  in  preliminary 
design. 

The  instrument  is  read  by  one  of  the  mirror  and  scale  methods, 
so  if  D  be  taken  in  scale  units, 

D  =  K  [  2Vd  +  d2  ]  (8) 

An  equivalent  expression  is  frequently  used, 

(9) 

Here,  Vi,  V%  and  V  are  the  potentials  of  the  two  sets  of  quad- 
rants and  of  the  needle  respectively. 

If  the  potential  differences  are  alternating,  the  instantaneous 
value  of  the  turning  moment  is  proportional  to  2V  d  +  d2  and 

D  = 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    251 

The  above  demonstration  is  in  general  sufficient;  in  it  all 
contact  differences  of  potential  have  been  neglected  and  it  has 
been  assumed  that  the  rates  of  change  of  the  capacities  of  the 
condensers  formed  by  the  quadrants  G  and  F  and  the  needle, 
as  the  latter  turns,  are  the  same  and  equal  to  that  when  the  needle 
is  in  its  zero  position.  If  this  is  not  so  there  will  be  an  additional 
moment  on  the  needle,  proportional  to  the  difference  of  the  rates 
of  change  of  the  capacities  of  the  two  condensers,  F  and  (7,  and 
to  y2;  as  this  moment  is  dependent  on  the  voltage  applied  to 
the  needle  it  will  vary  with  the  uses  to  which  the  instrument  is 
put.1 

The  Mechanical  and  Electrical  Zeros. — When  the  needle  and 
the  two  sets  of  quadrants  are  at  the  same  potential,  there  will 
be  no  electrical  turning  moment  acting  on  the  needle  and  it  will 
take  up  a  position  due  to  the  suspension  alone;  this  is  the  me- 
chanical zero  of  the  instrument. 

When  the  electrometer  is  perfectly  symmetrical,  if  the  two 
sets  of  quadrants  are  kept  at  the  same  potential  and  voltage  is 
applied  between  them  arid  the  needle,  it  will  be  seen  from  (6) 
that  there  should  be  no  deflection  from  the  mechanical  zero.  How- 
ever, the  slightest  departure  from  symmetry  will  cause  a  de- 
flection and  the  needle  will  move  to  the  electrical  zero.  The 
difference  of  the  two  zeros  should  be  small  and  in  a  carefully 
made  instrument  they  can  be  made  to  coincide  by  adjusting  the 
symmetry  of  the  arrangement.  In  the  instrument  shown  in 
Fig.  189,  this  may  be  done  by  tilting  the  upper  quadrants  by  the 
use  of  the  vertical  screw.  The  deflection  should  be  read  from 
the  electrical  zero. 

General  Considerations. — To  obtain  a  good  law  of  deflection 
over  a  long  range,  it  is  necessary  that  the  needle  be  bounded  by 
arcs  of  circles  and  straight  lines  as  indicated  in  Fig.  136.  Rais- 
ing or  lowering  the  needle  (or  any  tilting  of  the  needle)  will  cause 
a  change  in  the  constant ;  for  this  reason,  it  is  sometimes  preferable 
to  have  a  considerable  distance  between  the  upper  and  lower 
quadrants.  The  consequent  decrease  in  the  deflecting  moment 
must  be  compensated  by  using  a  more  delicate  suspension.  Even 
when  the  greatest  care  is  exercised,  the  constant  of  the  instru- 
ment will  not  be  the  same  for  all  deflections. 

If  the  instrument  is  to  be  used  for  alternating-current  meas- 


252 


ELECTRICAL  MEASUREMENTS 


urements,  the  calibration  should  be  made  by  using  alternating 
potential  differences,.  The  effects  of  contact  differences  of 
potential  are  then  eliminated.  Conditions  which  distort  the 


Variation  of  Sensitivity  with  Potential  of  Needle 
and  Distance  between  Quadrants 


400       800     1200     1GOO     2000     2400     2800    3200    3600 
Potential  of  Needle  in  Volts 

FIG.  137. — Illustrating  effect  of  distortion  of  the  electrostatic  field  at  the 
needle  of  a  quadrant  electrometer. 

electrostatic  field  in  which  the  needle  swings  cause  departures 
from  the  theoretical  law.  For  instance,  in  one  of  the  older  de- 
signs of  instrument,  a  guard  tube  was  used  which  surrounded 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    253 

the  stiff  wire  supporting  the  needle,  the  intent  being  to  protect 
the  movable  system  from  extraneous  electrostatic  attraction. 
The  whole  tube  was  supported  from  above,  and  carried  down 
through  the  circular  opening  at  the  center  of  the  quadrants,  being 
cut  away  at  the  sides  to  allow  free  motion  of  the  needle.  This 
construction  resulted  in  the  peculiar  law  of  deflection  shown  in 
Fig.  137. 

Electrostatic  Voltmeters. — On  the  supposition  that  the  law  of 
the  quadrant  electrometer  is  that  previously  deduced,  if  the 
needle  and  one  set  of  quadrants  are  connected  together,  V  =  0 
and 

D  =  Kd*. 

Or,  if  the  P.D.  is  rapidly  alternating, 

D  =  K1T  [\d*)dt. 

As  one  pair  of  quadrants  produces  no  effect,  it  may  be  omitted 
in  an  instrument  designed  primarily  for  voltage  measurements. 

As  the  deflections  are  proportional  to  the  mean  square  value 
of  the  P.D.,  electrostatic  voltmeters  are  particularly  applicable 
to  the  measurement  of  alternating  potential  differences. 

These  instruments  absorb  no  power  and  at  ordinary  frequencies 
produce  no  disturbance  of  the  potential  difference  to  which  they 
are  applied.  Their  action  is  not  complicated  by  inductance 
effects  so  there  are  no  frequency  or  wave-form  errors.  They 
have  no  self -heating  errors  and  are  uninfluenced  by  local  mag- 
netic fields.  On  the  other  hand,  at  low  voltages  the  forces 
to  be  dealt  with  are  very  small  and  consequently  the  instruments 
are  much  more  delicate  than  those  based  on  the  electrodynamo- 
meter  principle.  When  they  are  used  on  direct-current  circuits, 
the  effect  of  contact  differences  of  potential  must  be  eliminated  by 
reversals. 

Ayrton,  Mather  and  others  have  developed  the  electrostatic 
voltmeter  so  that  it  has  become  an  instrument  of  great  value  in 
laboratory  work.  Fig.  138  shows  one  of  Ayrton  and  Mather's 
instruments  for  low  voltages,  up  to  16  volts. 

This  instrument  is  intended  to  be  read  by  one  of  the  mirror 
and  scale  methods.  The  suspended  system  consists  of  a  light 


254 


ELECTRICAL  MEASUREMENTS 


aluminum  needle,  made  in  the  form  of  a  portion  of  a  cylinder. 
The  " quadrants"  are  portions  of  two  cylinders,  concentric  with 
the  needle.  The  needle  is  drawn  into  the  space  between  them  by 


Calibration  Curve 
for 
Reflecti  ng  Electrostat 
Voltmeter 

c 

— 

X-* 

* 

X* 

x-^" 

x 

x^ 

x 

/ 

/ 

/ 

/ 

/ 

0     1 


234567 
Deflections 


8     9    10  11 


FIG.   138. — Low-range    electrostatic  voltmeter  and  the  calibration  curve. 
Damping,  magnet  not  used  in  this  instrument. 

the  electrostatic  attraction.  The  controlling  force  is  given  by 
a  flat  strip  suspension  and  the  zero  may  be  set  by  means  of  a 
tangent  screw. 


FIG.   139. — Electrostatic  voltmeter  for  switchboard  work. 

In  order  to  damp  the  instrument,  the  needle,  which  from  its 
construction  forms  a  closed  loop,  is  frequently  arranged  to  turn 
between  the  poles  of  a  permanent  magnet. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    255 


To  prevent  extraneous  electrostatic  action,  the  needle,  the 
magnet  and  the  case  are  connected  together  electrically.  With 
this  construction,  the  outside  case  is  at  the  potential  of  one 
side  of  the  line.  In  later  instruments,  the  shielding  is  accom- 
plished by  an  inner  case  which  is  insulated  from  the  outside 
or  protective  case.  The  construction  of  the  instrument  is  such 
that  accidental  contact  between  the 
quadrants  and  the  movable  system 
is  impossible. 

Instruments  of  this  general  design 
are  listed,  which  give  a  full-scale  de- 
flection with  7  volts. 

In  cases  where  the  voltage  is  high, 
above  800  volts,  the  forces  become 
great  enough  so  that  the  cylindrical 
needle  may  be  pivoted  on  jewelled 
bearings  with  its  axis  horizontal  (see 
Fig.  139). 

The  controlling  moment  is  obtained 
by  using  a  small  weight  attached  to 
a  short  arm  which  projects  from  the 
axis.  Electrical  connection  with  the 
needle  is  made  by  a  very  fine  wire, 
wound  in  a  flat  spiral. 

Some  control  over  the  law  of  de- 
flection may  be  obtained  by  shaping 
the  quadrants. 

To    prevent    arcing    between    the       FlG-   140.— Working  parts 
ji  i    ,1  .  of   Kelvin  multicellular  elec- 

needle  and  the  quadrants   in  event    trostatic  voltmeter. 

of    a    great    increase    of    voltage,    a 

spark  gap  is  provided  between  the  terminals  and  within  the 
case.  It  is  intended  that  it  act  when  the  voltage  has  risen  to 
twice  the  full-scale  value.  Fuses  which  are  enclosed  in  the  re- 
movable terminals  are  thus  blown  and  the  instrument  automat- 
ically taken  out  of  circuit. 

A  reference  pointer  and  means  for  clamping  the  movable  system 
during  transportation  are  provided.  The  damping  is  obtained 
by  having  attached  to  the  needle  an  aluminum  sector  which 
moves  between  the  poles  of  a  permanent  magnet.  All  of  the 


256  ELECTRICAL  MEASUREMENTS 

working  parts  of  the  instrument  are  insulated  from  the  outside 
or  protecting  case.  This  removes  the  possibility  of  incurring 
shocks  when  the  instrument  is  touched. 

To  increase  the  forces  acting  on  the  movable  systems  of 
electrostatic  voltmeters,  up  to  about  1,000  volts,  Lord  Kelvin 
devised  the  multicellular  instrument,  an  example  of  which  is 
shown  in  Fig.  140. 

A  torsion  wire  suspension  is  used,  and  the  increase  of  the 
deflecting  force,  which  is  in  proportion  to  the  number  of  cells, 
is  sufficient  so  that  a  pointer  and  scale  may  be  used  for  reading 
the  deflections.  The  instrument,  however,  is  not  portable  in 
the  ordinary  sense.  In  the  voltmeter  shown  in  Fig.  140  the 
damping  is  effected  by  a  disc  which  turns  in  a  viscous  oil  con- 
tained in  a  little  glass  vessel  at  the  bottom  of  the  instrument. 

Two  vertical  plates  are  connected  to  the  movable  system 
and  screen  it  from  the  action  of  the  set  of  quadrants  near  which 
they  are  placed. 

Use  of  a  False  Zero  Reading. — It  is  sometimes  desirable  to 
measure  a  small  direct-current  voltage  without  drawing  any 
current.  The  use  of  the  electrostatic  voltmeter  suggests  itself 
but  the  normal  curve  of  the  reflecting  form  of  this  instrument  is 
very  nearly  a  parabola,  -as  is  shown  by  Fig.  138,  so  that  a  low 
potential  difference  gives  a  very  small  deflection  which  cannot 
be  read  with  accuracy.  The  difficulty  may  sometimes  be  over- 
come by  superposing  the  P.D.  to  be  measured  on  a  fixed  and  higher 
voltage.  For  instance,  if  the  instrument  gives  a  scale  reading  of 
50  cm.  with  50  volts,  a  potential  difference  of  2  volts  applied 
directly  to  the  instrument  will  give  a  deflection  of  0.08  cm. 
However,  if  it  be  superposed  on  a  P.D.  of  50  volts  the  increase  in 
deflection  will  be  4.08  cm.  As  the  upper  part  of  the  calibration 
curve  is  nearly  straight,  the  deflections  from  the  false  zero  are 
practically  proportional  to  the  voltage. 

Condenser  Multipliers  for  Extending  the  Range  of  Electro- 
static Voltmeters. — The  range  of  an  electrostatic  voltmeter  may 
be  extended  by  means  of  condenser  multipliers  as  indicated  in 
Figs.  141  and  142. 

A  condenser  of  the  proper  capacity  may  be  joined  in  series  with 

( C*      —I—  C^  \ 

the  voltmeter.     Then  V  =  Vz—         —where  F2  is  the  reading 

CA/ 

• 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    257 


of  the  instrument  and  CM  and  Cv  are  the  capacities  of  the  con- 
denser and  the  voltmeter  respectively.     As  the  capacity  of  the 

(C1      I    n   \ 
instrument,  CV,  depends  on  the  deflection,  the  factor— 

Cjif 

will  not  be  a  constant  and  the 
voltmeter  must  be  calibrated 
with  the  condenser  in  place. 

An  alternative  method  is  to 
join  a  number  of  condensers  in 


HH 


FIG.  142. 
FIGS.  141  AND  142. — Condenser  multipliers  for  electrostatic  voltmeter. 

series  and  to  place  the  electrostatic  voltmeter  around  one  of  them, 
as  shown  in  Fig.  142. 

Here  again  the  whole  arrangement  should  be  calibrated  as  a 
unit. 


FIG.  143. — Electrostatic  voltmeter  with  variable  range. 

A  simple  form  of  electrostatic  voltmeter  with  a  gravity  control, 
a  very  obvious  development  from  the  quadrant  electrometer, 
is  shown  in  Fig.  143. 

17 


258 


ELECTRICAL  MEASUREMENTS 


The  range  of  the  instrument  is  up  to  10,000  volts,  without  the 
use  of  a  condenser  multiplier,  and  up  to  30,000  volts  if  the 
multiplier  is  employed.  The  deflection  per  volt  may  be  varied 
by  means  of  weights  which  are  hung  on  the  hook  at  the  lower  end 
of  the  needle.  The  oscillation  of  the  needle  can  be  checked  by 
bringing  a  silk  thread  into  contact  with  the  pointer. 

Fig.  144  shows  a  form  of  electrostatic  voltmeter  made  by 
Siemens  and  Halske  for  voltages  up  to  150,000. 

One  electrode,  A,  is  under  the  base  of  the  glass  jar  C;  this  jar 
is  filled  with  oil  and  the  movable  elec- 
trode B  is  suspended  in  it.  The  restor- 
ing force  is  a  spiral  spring.  The  pull  on 
the  electrode  B  is  transmitted  to  the 
pointer  by  a  mechanism  which  is  so 


,  1.  FIG.   144. — Siemens  and  Halske  high-range  electrostatic  voltmeter. 

arranged  that  the  upper  70  per  cent,  of  the  scale  is  practically 
uniformly  divided.  The  use  of  the  oil  reduces  the  risk  of  an  arc 
forming  between  the  electrodes  A  and  B  and  permits  them  to  be 
brought  nearer  together,  thus  increasing  the  force  and  permitting 
the  instrument  to  be  made  smaller.  The  damping  is  by  the  fluid 
friction  of  B.  The  shields  D  and  D'  are  to  protect  the  instru- 
ment from  the  influence  of  surrounding  objects. 

The   Westinghouse   Co.    manufactures   the  high-range   volt- 
meter2 shown  diagrammatically  in  Fig.  145. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    259 


The  voltage  is  applied  at  7  and  /';  between  ab  and  6c  are  two 
condensers  which  can  be  short-circuited  at  will,  thus  altering 
the  range  of  the  instrument.  They  are  placed  within  the  highly 
insulated  condenser  terminal,  T,  and  are  brought  into  action  by 
means  of  a  silk  cord.  The  fixed  attracting  elements  are  at 
B  and  B1 '.  The  movable  element  consists  of  two  hollow  metal 
cylinders  M  and  M'  which  are  united  by  a  suitable  web.  This 
system  hangs  freely  from  a  single  pivot  resting  in  a  jewel.  The 
usual  controlling  spring  and  zero  adjustment  are  provided. 

There  is  no  electrical  connection  to  the  movable  element; 
on  the  application  of  the  voltage,  charges  are  induced  on  it. 


W 


Diagrammatic  Arrangement 

of  High-Tension 
Electrostatic  Voltmeter 


80  Kilovolt  Settiug,  Curve  "a"  Kilovolts 

S  8  g  s  8  §  3 

*           ,  ILJU-II- 

i>       1               Immr 

JL_LK\_Ma 

y 

3  &  8  8,8  & 
ilovolt  Setting,  Curve'  b"  Kilobit. 

£L 

4 

. 

Diagram  of  Connections  of  Voltmeter 

^ 

"7_ 

^ 

n? 

^ 

^ 

/ 

^ 

120,  or 

(a)  8 

(6)4 

With 

Metei 
bcale 

CALIBRATION  CURVES  OF 
0  VOLT  WESTINCHOUSE  ELECTROSTATIC 
VOLTMETER 
0  Kilovolt  Setting.  Condense»"a"short 
Circuited 
0  Kilovolt  Betting,  Condensers  Vand"6 
Short  Circuited 
Neither  Condenser  Short  Circuited,  the 
Reads  Directly  in  Kilovolts  on  Lower 

z 

5 

/ 

10 


90       100 


20        30        40        50        60        70 

Division's  on  Upper  Uniform  Scale 

FIG.  145.  —  Westinghouse  high-range  electrostatic  voltmeter. 

As  the  curved  plates  B  and  B'  and  the  movable  parts  are  not 
concentric,  the  latter  will  move  so  as  to  increase  the  electro- 
static capacity  of  the  arrangement;  that  is,  in  the  direction  of 
the  arrow.  The  plates  B  and  B'  are  so  bent  that  the  scale  is 
approximately  uniform  over  a  considerable  portion  of  its  length. 
All  the  working  parts  are  immersed  in  oil,  and  as  the  movable 
element  is  hollow,  the  weight  is  practically  removed  from  the 
jewel  and  pivot. 

These  voltmeters  are  made  for  potentials  as  high  as  200,000 
volts.  Instruments  having  a  range  of  25,000  volts,  both  con- 
densers being  short-circuited,  will  read  up  to  100,000  volts  with 
both  condensers  in  service. 


260 


ELECTRICAL  MEASUREMENTS 


THE  SPARK  GAP  METHOD  OF  MEASURING  HIGH  PEAK 
VOLTAGES 

It  is  difficult  to  design  indicating  instruments  for  directly  deter- 
mining extra  high  voltages  because  of  corona  effects,  disruptive 
discharges,  and  extraneous  electrostatic  attractions.  Also  in 
testing  the  dielectric  strengths  of  insulations  it  is  desirable  to 
know  the  maximum  rather  than  the  effective  voltage  to  which 
any  sample  is  subjected.  Consequently  a  method  of  meas- 
urement depending  on  the  dielectric  strength  of  air  has  been 
developed  and  has  been  employed  for  many  years.  The  neces- 


FIG.  146. — Needle-point  spark  gap. 

sary  apparatus  is  termed  a  spark  gap  and  its  use  as  a  means  of 
determining  high  voltages  is  sanctioned  by  the  American  Institute 
of  Electrical  Engineers3.  This  method  is  frequently  used  in 
acceptance  tests  of  new  apparatus  where  the  dielectric  strength 
of  the  insulation  is  guaranteed. 

The  construction  of  a  needle-point  spark  gap  is  shown  in  Fig. 
146.  According  to  the  standardization  rules  of  the  American 
Institute  of  Electrical  Engineers,  "the  spark  points  should  con- 
sist of  new  sewing  needles  supported  at  the  ends  of  linear  con- 
ductors which  are  each  at  least  twice  the  length  of  the  gap. 
There  should  be  no  extraneous  body  near  the  gap  within  a  radius 
of  twice  its  length." 

The  arrangement  is  such  that  the  points  of  the  needles  may 
be  set  at  any  desired  distance  apart.  The  function  of  the  carbon 


MEASUREMENT tOF  POTENTIAL  DIFFERENCE    261 


resistances  placed  vertically  above  the  supporting  pillars  is  to 
limit  the  current  when  the  gap  breaks  down.  The  establishment 
of  surges  in  the  circuit  due  to  a  sudden  change  in  its  constants  is 
thus  avoided.  Water-tube  resistances  are  more  reliable  for  this 
purpose  than  carbon  rods,  which  may  have  low  resistances  at 
high  voltages. 

The  current  after  the  gap  has  broken  down  should  not  be 
greater  than  1  amp.  The  needles  are  set  in  accordance  with 
the  table  given  below. 

To  use  the  gap,  it  is  set  to  correspond  with  the  appropriate 
voltage  and  placed  in  parallel  with  the  apparatus  under  test. 
The  applied  voltage  is  then  gradually  raised  until  the  gap  breaks 
down.  The  reading  of  the  voltmeter  on  the  low-tension  side 
of  the  testing  transformer  and  the  adjustment  of  the  voltage 
regulating  apparatus  at  the  instant  of  breakdown  are  noted.  A 
new  set  of  needles  is  then  inserted  and  the  gap  set  for  a  voltage 
about  20  per  cent,  too  high.  The  former  reading  of  the  voltmeter 
or  the^adjustment  of  the  regulating  apparatus  is  then  repro- 
duced and  the  voltage  applied  for  the  required  time. 

The  gap  breaks  down  at  the  peak  of  the  wave  and  therefore 
gives  a  measure  of  the  maximum  voltage  to  which  the  insulation 
has  been  subjected.  It  will  do  this  irrespective  of  the  wave 
form,  but  the  following  table  is  for  sinusoidal  waves  and  effective 
voltages.  If  the  gap  is  to  be  set  for  peak  voltages,  the  values  in 
the  table  must  be  multiplied  by  \/2. 

TABLE  I. — NEEDLE-POINT  SPARK-OVER  VOLTAGES   WITH  No.   00  SEWING 

NEEDLES 
(At  25°C.  and  760  mm.  barometer — relative  humidity  80  per  cent.) 


R.m.s.  kilovolts 

Millimeters 

R.m.s.  kilovolts 

Millimeters 

10 

11.9 

40 

62 

15 

18.4 

45 

75 

20 

25.4 

50 

90 

25 

33.0 

60 

118 

30 

41.0 

70 

149 

35 

51.0 

80 

180 

The  American  Institute  of  Electrical  Engineers  sanctions  the 
use  of  the  needle-point  sparl^  gap  for  voltages  between  10  and 
50  kv. 


262 


ELECTRICAL  MEASUREMENT^ 


70 


CO 


40 


I- 


20 


10 


Lt 


Mechanically,  the  needle-point  spark  gap  is  about  the  simplest 
electrical  measuring  device  but  this  simplicity  of  construction  is 
no  guarantee  of  simplicity  of  action  and  the  needle-point  gap 
must  be  used  by  skilled  experimenters  if  reliable  results  are  re- 
quired. Its  indications  are  open  to  many  sources  of  error. 
Like  all  spark  gaps,  it  is  influenced  by  the  distortion  of  the 

electrostatic  field  in  its  neigh- 
boorhood,  due  to  surrounding 
objects. 

For  high  voltages,  there- 
fore, the  arrangement  must 
necessarily  occupy  a  large 
space.  In  an  apparatus  for 
200  kv.,  if  designed  as  indi- 
cated above,  the  distance  be- 
tween the  needle  points  will 
be  about  52  cm.;  the  sup- 
ports for  the  needles  will  each 
be  about  104  cm.  long,  so  the 
length  of  the  apparatus  will 
be  at  least  9  ft.,  and  as  no 
object  should  be  nearer  the 
gap  than  3J^  ft.,  the  space 
occupied  would  be  about  9  by 
7  by  7  ft. 

In  addition  to  this  large 
space  factor,  which  is  disad- 
vantageous, there  are  irreg- 
ularities in  the  action  of  this 
form  of  gap  arising  from  the  varying  sharpness  of  the  needles. 
A  new  set  of  needles  must  be  inserted  after  each  breakdown  of 
the  gap. 

When  the  voltage  is  gradually  raised,  the  points  are  seen  to 
be  surrounded  by  a  bluish  glow  or  corona,  more  or  less  spherical 
in  form.  This  happens  long  before  the  gap  breaks  down  and 
means  that  the  air  about  the  points  has  become  -conducting. 
Serious  errors  may  be  introduced  by  this  preliminary  breaking 
down  of  the  air,  for  irregularities  due  to  heating  are  thus  intro- 
duced. Again,  it  is  found  in  all  cases  where  the  corona  forms 


0     20    40    GO     80    100  120  140  160  180 
Spark  Gap  in  Millimeters 

FIG.  147.— Plot  of  A.  I.  E.  E.   table 
for  needle-point  spark  gap. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    263 


before    the    passage   of   the 
spark    that     the    dielectric 
strength    of   an    air   gap   is      20° 
very  dependent  on    the  hu- 
midity.    This  is  illustrated      m 
by  Fig.  148.                                   160 
The  density  of  the  air  af-      i50 
fects    the    results   obtained      HO 
with  any  form  of  spark  gap.   ^  iso 
The   irregularities  of  the   1  12° 
needle-point     gap    have  g110 
proved   so  troublesome  that    s 
a  substitute  for  this  form  of   |  go 
gap  has  been  sought.     For   *  70 
voltages   above   50  kv.  the        GO 
use    of    two   spherical   elec-       so 
trodes  of  equal  diameters  is       40 
now   recommended   by   the 
American  Institute  of  Elec- 
trical   Engineers.     The   ad-        0 
vantage  is  that  if  the  dis- 
tance between  the  electrodes      Fir 

Humi-dity 
Per  cent 

A 

i 

p§ 

/ 

// 

'  / 

// 

u 

/ 

2 

// 

/ 

J/f 

7 

n 

'•/f 

/ 

j 

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I 

//, 

// 

/ 

y/, 

/ 

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$/ 

/> 

y/ 

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It 

I/ 

w 

/ 

i 

f\ 

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j 

3    5    10  15   20  25   30  35  40    45  50  55  G( 
Spacing  in  cm 
.    148.  —  Showiner  effect  of  hnmirlil 

0.354 


is  less  than  three  times  the  on  the  action  of  a  needle-point  spark 

radius   of  the   spheres,    the  gap 

corona  does  not  form  before  the  gap  breaks  down.     The  erratic 

effects  due  to  broken  down 
air  around  the  electrodes  are 
thus  avoided.  Humidity  has 
no  influence  on  the  results. 

An  additional  advantage  is 
that  the  length  of  the  gap  is 
much  reduced;  with  spheres 
25  cm.  in  diameter,  the  spark- 
ing distance  for  200  kv.  is 
about  13  cm.  against  about 
52  cm.  for  the'  needle-point 

Note: 

A  variation  of  1  cm.  in  thickness  and  gaP  • 

width  of  wooden  parts  is  permissible  rpn  i 

^      1/ln     e     ,  .    ,        The  sphere  gap  is  especi- 

FIG.  149. — Spark  gap  with  spherical 

electrodes.  ally    adapted    for  measuring 


264  ELECTRICAL  MEASUREMENTS 

extra  high  voltages,  above  50  kv.  It  is  not  so  well  adapted  for 
low  voltages  for  the  spheres  must  be  brought  very  near  together. 

The  spheres  should  be  at  least  twice  the  gap  distance  from 
surrounding  objects  and  greater  than  this  if  one  sphere  is 
grounded. 

If  the  current  be  limited  to  less  than  1  amp.  by  water-tube 
resistances,  pitting  of  the  spheres  is  avoided  and  they  need  be 
repolished  only  occasionally. 

When  neither  sphere  is  grounded,  it  is  possible  to  calculate 
mathematically  the  relation  between  the  breakdown  voltage  and 
the  length  of  gap.  The  dielectric  stress  will  be  a  maximum  at 
the  points  where  the  line  joining  the  centers  of  the  spheres  cuts 
their  surfaces.  If  the  value  of  the  potential  gradient  at  this 
point  be  denoted  by  g,  then  it  may  be  shown  that 

g  =   (?)  ;       kv'/Cm-  (11) 

V  is  the  potential  difference  and  x  the  distance  apart  of  the 

y 
surfaces.      —  is  therefore  the  average  potential  gradient;  /  is  a 

factor  which  depends  on  x  and  the  radius  of  the  spheres,  a; 
it  is  the  quantity  which  must  be  multiplied  into  the  average 
gradient  to  give  the  maximum  gradient  and  has  been  expressed 
in  the  form  of  an  infinite  series  by  A.  Russell5. 

TABLE  II. — VALUES  OF  /,    NEITHER  SPHERE    GROUNDED,   COMPUTED  BY 

A.  RUSSELL 

a 

0.0 1.000 

0.1 1.034 

0.2 1.068 

0.3 1.102 

0.4 1.137 

0.5 1.173 

0.6 '.  ..  1.208 

0.7 1.245 

0.8 1.283 

0.9 1.321 

1.0 1.359 

1.5 1.559 

2.0 1.770 

3.0 2.214 

4.0 2.677 

These  values  are  plotted  in  Fig.  150. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    265 

When  the  potential  between  the  spheres  is  gradually  raised, 
it  would  naturally  be  expected  that  the  gap  would  break  down 
when  the  maximum  gradient  reached  some  definite  value,  gs, 
and  that  if  this  value  be  known  the  voltage  corresponding  would 
be 

V  =  </*  7  (12) 


E 

ove 
the 

4.2 

3.8 

3.4 
3.0 
2.6 

s 

2.2 
1.8 
1.4 
1.0 

experiment  shows  that  gs,  the  maximum  gradient  at  spark- 
r,  depends  upon  the  radius  of  the  spheres,  being  larger  as 
radius  is  diminished.     F.  W.  Peek  has  shown  that  betweer 
the  limits  x  =  0.54\/a  and  x  =  2c 

€ 

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27.2  (  1  4 
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*/«  Radius 

FIG.  150. — Plots  of  /  for  spark        FIG.  151. — Showing  relation  of  maxi- 
gap  with  spherical  electrodes.      mum  potential  gradient  at   spark-over 

to  radius  of  spheres. 


This  relation  is  shown  graphically  in  Fig.  151. 


If  —  is  greater 


than  4,  corona  forms  before  the  breakdown  and  the  above  equa- 
tions are  no  longer  applicable. 

If  one  sphere  is  grounded,  the  electrostatic  field  is  so  dis- 
torted by  the  supporting  stems  and  surrounding  objects  that  the 
value  of  /  deduced  from  purely  mathematical  considerations  is 


266  ELECTRICAL  MEASUREMENTS 

no  longer  applicable.  In  this  case,  experimentally  determined 
values,  /o  (see  Fig.  150),  must  be  used.  They  are  deduced  on 
the  assumption  that  at  spark-over,  gs  is  as  given  by  Fig.  151. 

Variations  of  frequency,  at  least  up  to  1,000  cycles,  have  no 
influence  on  the  results. 

As  an  example  of  the  use  of  the  foregoing,  the  voltage  necessary 
to  break  down  a  10-cm.  gap  between  spheres  25  cm.  in  diameter, 
neither  sphere  being  grounded,  will  be  calculated.  Assuming 
the  barometric  pressure  to  be  760  mm. 

0.54   \  W 

l+-7==)  =31.4  kv' 


cm. 


*  -08 

a  "  12.5  ' 

/  =  1.283  by  table. 
31.4  •   10 


For  a  sinusoidal  wave  V  =  173  kv.  effective. 

If  the  spheres  are  25  cm.  apart  and  one  of  them  is  grounded,  the 

calculation  is 

0.  =  31.4  — 
cm. 


a       12.5 

/o  =  2,  from  Fig.  150. 

/.  V  =  3L42    25  =  392  kv.  max. 

For  a  sinusoidal  wave  V  =  277  kvr  effective. 

Reference  to  Fig.  151  shows  that  in  important  work  it  is  best 
to  use  large  spheres  and  thus  avoid  the  use  of  the  steep  part  of 
the  curve  and  the  consequent  uncertainty  in  gs. 

In  practical  work  it  is  best  to  take  the  spark-over  voltages  from 
experimentally  determined  'curves,  or  the  table  given  on  page 
267,  rather  than  to  use  the  above  formulae. 

The  use  of  a  spark  gap  is  not  without  danger  to  the 
apparatus  under  test;  for  high  voltage  surges  may  be  set  up 
when  the  gap  breaks  down,  hence  the  use  of  the  current-limiting 
resistances. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    267 


In  using  any  form  of  spark  gap  it  is  essential  that  all  chance 
of  accidental  circuit  variations  be  eliminated.  If  this  is  not  done, 
the  observer  may  be  misled  by  the  breaking  down  of  the  gap  due 
to  high-voltage  oscillations.  The  sphere  gap  is  especially 
susceptible  to  circuit  variations;  consequently  all  accidental 
spark  discharges  from  the  testing  circuit  must  be  avoided. 

The  following  table  from  the  Standardization  Rules  of  the 
American  Institute  of  Electrical  Engineers  is  based  on  the  ex- 
perimental work  of  Peek,  Chubb  and  Fortescue. 

SPHERE-,GAP  SPARK-OVER  VOLTAGES 
(At  25°C.  and  760  mm.  barometric  pressure) 


Kilo- 
volts 
effective 

bparking  distance  in  millimeters 

62.5-mm.  spheres 

125-mm.  spheres 

250-mm.  spheres 

500-mm.  spheres 

One 
sphere 
grounded 

Both 
spheres 
insulated 

One 
sphere 
grounded 

Both 
spheres 
insulated 

One 

sphere 
grounded 

Both 
spheres 
insulated 

One 

sphere 
grounded 

Both 
spheres 
insulated 

10 
20 
30 

4.2 
8.6 
13.5 

4.2 
8.6 
13.5 

14.1 

14.1 

40 
50 
60 

19.2 
25.5 
34.5 

19.2 
25.0 
32.0 

19.1 
24.4 
30.0 

19.1 
24.4 
30.0 

29 

29 

70 
80 
90 

46.0 
62.0 

39.5 
49.0 
60.5 

36.0 
42.0 
49.0 

36.0 
42.0 
49.0 

35 
41 

46 

35 
41 
45 

41 
46 

41 
45 

106 
120 
140 





56.0 
79.7 
108.0 

55.0 
71.0 
88.0 

52 
64 

78 

51 
63 

77 

52 

63 

74 

51 
62 
73 

160 
180 
200 



150.0 

110.0 
138.0 

92 
109 
128 

90 
106 
123 

85 
97 
108 

83 
95 
106 

220 
240 
260 

150 
177 
210    . 

141 
160 
180 

120 
133 
148 

117 
130 
144 

280 
300 
320 

250 

203 
231 
265 

163 
177 
194 

158 
171 

187 

340 
360 
380 

214 
234 
255 

204 
221 
239 

400 

276 

257 

The  values  in  the  above  tables  are  corrected  for  temperature 
and  barometric  pressure  as  follows.  To  find  the  spacing  at 
which  it  is  necessary  to  set  a  gap  to  spark  over  at  some  re- 


268 


ELECTRICAL  MEASUREMENTS 


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One,  Sphere  Grounded 

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20  40  GO  80          100 

Sparking  Distance  in  Millimeters 


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Curve  Z?-One  Sphere  .Grounded 

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CO  90  120         150 

Sparking  Distance  in  Millimeters 


340 
320 
300 
280 
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/        25°C.  76  mmi  Bar.  Pressure 
/                           1 

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C 
C 

urve  >l-Both  Spheres  Insulated 
urve  .B-One  Sphere  Grounded 

/ 

:r 

\  \ 

\  \ 

0  50          100          150         200         250  0 

Sparking  Distance  in  Millimeters 

FIG.  152. — Plots  of  A.  I.  E.  E.  table  for  spark  gap  with  spherical  electrodes. 


50          100         150          200         250 
Sparking  Distance  in  Millimeters 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    269 

quired  voltage  divide  the  required  voltage  by  the  correction 
factor 

0.3926 
~  273  +T 

b  is  the  barometric  pressure  in  millimeters  .and  t  the  temperature 
in  degrees  C.  A  new  voltage  is  thus  obtained.  The  spacing 
corresponding  to  this  new  voltage  as  obtained  from  the  table 
is  that  required. 

The  voltage  at  which  a  given  gap  sparks  over  is  found  by 
taking  the  voltage  corresponding  to  the  spacing  from  the  table 
and  multiplying  by  the  above  correction  factor. 


POTENTIOMETER  ARRANGEMENTS 

Poggendorf  Method  of  Comparing  a  Potential  Difference 
and  an  Electromotive  Force. — All  of  the  various  methods  now 
used  for  the  rapid  standardization  of 

r  Et\  Jo-i 

direct-current  instruments  depend  on 

the   ability  to   compare   a   potential 

difference  with  an  e.m.f.     This  may 

be     accomplished    by    Poggendorfs 

method,    which    is   shown   diagram- 

matically  in  Fig.  153.     E\  and  E2  are 

the  e.m.fs.  of  the  batteries  at  EI  and 

E2.     The  cell  at  EI  will  of  necessity       FIG.    153. — Connections 

have  the  higher  e.m.f.     Ri  and  Rz  are 


two  variable  resistances,  K  a  key  ence  with  an  electromotive 
which  is  normally  open,  and  G  a  suit- 
able galvanometer.  The  circuit  of  EI  is  closed  through  the  re- 
sistance RI  +  R2,  across  which  there  will  be  established  a  poten- 
tial difference,  P.D.  Suppose  the  key  K  to  be  open.  Then  the 
current  in  Ri  is  the  same  as  that  in  R2,  and  its  value  is 


P.D. 

Rl  ~T~ 


I    =    •= 


The  potential  difference  between  the  ends  of 
be 


will  consequently 


270  ELECTRICAL  MEASUREMENTS 

This  may  be  varied  by  altering  either  Ri  or  R2.  The  battery 
Ez  is  so  inserted  that,  when  the  key  is  depressed,  its  e.m.f. 
opposes  the  potential  difference  due  to  the  passage  of  the  cur- 
rent through  Ri.  If  by  varying  Ri  or  R2  this  potential  differ- 
ence is  made  equal  to  E2,  no  current  will  flow  through  the  gal- 
vanometer and  the  battery  E2  when  the  key  is  closed. 
Consequently  the  absence  of  a  deflection  of  the  galvanometer 
when  the  circuit  is  closed  shows  that 


= 
or 

E2 


P.D.  ~  Ri  + 

If  jRi  +  R2  be  so  high  that  very  little  current  flows  through 
the  battery  E2,  the  fall  of  potential  in  -Ei,  which  is  given  by 
IB,  where  B  is  the  battery  resistance,  will  be  so  small  that  the 
P.D.,  which  is  equal  to  Ei  -  IB,  may  be  taken  as  equal  to 
and 

E2  RI 

El  =  BHTR,'  V6r 
or 

RI  -\-  R 


The  larger  Ri  -f-  R2,  the  better  the  approximation. 

It  will  be  noticed  that  current  can  flow  through  E2  only  when 
the  key  is  depressed,  and  that  when  the  adjustment  is  perfect, 
there  can  be  no  current  through  the  battery  E2.  This  is  of 
importance,  for  if  care  be  exercised  it  allows  cells  to  be  used  at 
Ez  without  danger  of  altering  their  e.m.fs.  by  polarization. 

Much  labor  has  been  expended  in  the  development  and  study 
of  galvanic  cells,  suitable  for  use  at  E2)  which  shall  have  per- 
fectly definite  e.m.fs.,  and  consequently  can  be  used  as  standard 
cells  with  which  P.D.  or  EI  may  be  compared.  On  account  of 
their  high  degree  of  reproducibility  the  Clark  and  the  Weston  cells 
are  now  universally  used.  These  cells  are  of  the  open-circuit 
type  and  no  appreciable  current  can  be  drawn  from  them  without 
temporary  alteration  of  their  e.m.f. 

As  it  is  important  to  avoid  short-circuiting  EI  or  connecting 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    271 

it  through  a  small  coil  which  might  be  overheated,  it  is  well 
to  unplug  large  resistances  (1,000  ohms)  in  jfti  and  R2  before 
making  the  final  connections. 

The  key  should  not  be  left  depressed,  but  released  as  soon 
as  the  galvanometer  needle  begins  to  move.  The  direction  of  the 
motion  of  the  needle  must  be  noted  and  another  trial  made  with 
a  different  resistance  in  Rt.  The  direction  of  the  deflection 
depends  on  whether  Ri  is  too  large  or  too  small. 

After  repeated  trials  such  a  resistance  will  be  found  that  the 
galvanometer  will  not  deflect. 
Then 

#1  +  Ri 

Et\    =   &2 5 . 

til 

To  make  the  final  balancing,  either  Ri  or  R2  may  be  ad- 
justed. One  must  be  sure  that  all  plugs  are  firmly  inserted  and 
that  all  connections  are  perfect.  The  key  is  to  be  depressed  for 
as  short  a  time  as  possible. 

If  in  any  particular  case  the  standard  cell  is  higher  in  e.m.f. 
than  the  cell  to  be  compared  with  it,  the  procedure  must  be 
changed,  for  standard  cells  cannot  be  used  in  closed  circuits. 
In  this  case,  an  auxiliary  battery  having  a  higher  e.m.f.  than 
either  EI  or  E%  is  used  in  position  E\.  The  cells  are  compared 
with  it  in  succession,  or  else  the  circuit  is  so  arranged  that 
both  cells  can  be  compared  with  the  auxiliary  battery  at  the 
same  time.  The  latter  is  a  very  accurate  method,  for  it  obviates 
difficulties  arising  from  variations  of  the  current  through  RI 
and  Rz. 

The  Potentiometer. — In  the  section  on  ''Calibration  of  In- 
struments" some  methods  of  employing  standard  cells  are  dis- 
cussed, the  apparatus  for  which  may  be  assembled  in  any  well- 
appointed  laboratory  for  electrical  measurements.  In  general, 
it  is  much  more  convenient  to  use  for  the  purpose  pieces  of 
commercial  apparatus  called  potentiometers.  These  instruments 
are  all  more  or  less  convenient  arrangements  for  projecting 
potentials,  so  designed  as  to  be  direct-reading  for  voltages  up 
to  about  1.5  volts.  The  principle  involved  is  illustrated  by  Fig. 
154. 

ab  is  a  definite  resistance  along  which  the  slider  c  can  be  dis- 
placed. Rh  is  a  rheostat  by  which  the  current  in  ab  can  be 


272 


ELECTRICAL  MEASUREMENTS 


adjusted.  Let  r*i  be  the  resistance  from  b  to  c  when  the  galva- 
nometer deflection  is  zero  and  the  standard  cell  is  in  circuit,  and 
r2  the  reading  of  the  slider  when  the  galvanometer  deflection  is 
zero  and  the  switch  is  on  P.D.,  the  current  in  ab  being  as  before. 
It  is  necessary  that  the  current  Iab  be  constant.  To  ascertain^ 
this  is  so  necessitates  the  throwing  of  the  switch  to  E  and  the 
resetting  of  the  slider.  The  potentiometer  current  will  be 


and 


I nh    = 


P.D.= 


E 


An  obvious  improvement  is  to  tap  in  the  standard  cell  at  a 
fixed  point  on  ab',  if  the  e.m.fs.  of  all  cells  which  are  commonly 


FIG.  154. — Illustrating  the 
principle  of  the  potentiom- 
eter. 


FIG.  155.  —  Illustrating 
principle  of  potentiometer 
with  adjustment  for  standard 
cells  of  different  e.m.fs. 


employed  at  E  were  the  same  this  would  fix  the  value  of  Iab 
at  which  the  galvanometer  would  be  in  balance,  but  some  forms 
of  standard  cells  have  temperature  coefficients  and  the  Weston 
cell  in  its  commercial  form,  which  is  the  one  most  frequently 
used,  is  a  secondary  standard,  the  e.m.f.  of  which  varies  slightly 
with  different  cells.  The  resistance  between  the  cell  terminals 
must  therefore  have  a  slight  adjustment  if  Iab  is  always  to  be 
brought  to  a  definite  value.  The  arrangement  then  becomes 
that  shown  in  Fig.  155. 

Each  step  of  the  resistance  W  is  marked  with  the  standard- 
cell  e.m.f.  to  which  it  corresponds. 

lab  is  always  adjusted  to  some  predetermined  value.  There- 
fore E  =  I^  ri  where  n  is  the  resistance  between  c'  and  g.  The 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    273 

process  is  then  to  set  c'  so  that  the  drop  between  the  terminals  of 
the  standard-cell  circuit  due  to  the  predetermined  potentiometer 
current  will  be  equal  to  the  e.m.f .  of  the  particular  standard  cell 
used.  The  proper  value  of  Iab  is  obtained  by  manipulating 
the  rheostat,  Rh.  With  the  switch  S  thrown  to  the  right,  the 
correct  adjustment  is  shown  by  the  galvanometer  remaining  in 
balance.  After  this,  P.D.  is  measured  as  before  by  adjusting  c, 
the  switch  being  thrown  to  the  left.  To  test  the  value  of  Iab, 
it  is  necessary  to  insert  the  galvanometer  in  the  standard-cell 
circuit  by  the  double-throw  switch.  This  test  is  necessary  be- 
cause the  battery  may  not  be  constant. 

The  usual  range  of  a  potentiometer  is  from  0  to  about  1.5  volts; 
for  higher  voltages  it  is  necessary  to  use  it  in  conjunction  with  a 
volt  box.  This  consists  of  a  high  resistance  which  is  connected 
across  the  potential  difference  to  be  measured.  It  is  divided  by 
taps  so  that  the  potentiometer  measures  a  definite  fraction, 

Mo,  Moo,  M,ooo  of  P.D. 

Practical  Arrangement  of  the  Potentiometer. — In  order  that 
a  potentiometer  may  attain  its'  highest  usefulness,  it  must  be  so 
arranged  that  the  value  of  P.D.  may  be  read  directly  from  the 
position  of  the  slider  c,  no  calculation  being  necessary.  That 
this  is  possible  is  seen  from  the  fact  that  whenever  the  instrument 
is  used,  the  current  Iab  has  a  definite  value  and  therefore  the  drop 
from  b  to  any  point  on  the  wire  ab  is  always  the  same.  Conse- 
quently the  scale  from  which  the  position  of  c  is  read  may  be  so 
graduated  that  it  gives  the  drop  in  volts  between  b  and  the 
various  positions  of  c  directly. 

Much  ingenuity  has  been  expended  in  arranging  the  resistance 
ab  so  that  while  it  is  brought  into  a  small  compass  it  is  accessible 
at  practically  all  points.  The  simplest  method  of  doing  this  is 
shown  in  Fig.  156.  Fifteen  equal-resistance  coils  are  used  in 
series  with  a  slide  wire  whose  resistance  is  slightly  greater  than 
that  of  a  single  coil.  The  scale  of  the  slide  wire  is  divided  into 
1,100  equal  parts  and  the  resistance  of  the  whole  affair  may  be 
about  75  ohms. 

The  slide  wire,  represented  by  DB,  is  wound  in  a  screw-thread 
on  a  marble  cylinder  6  in.  in  diameter;  it  consists  of  11  turns 
with  a  total  resistance  of  5.5  ohms,  and  is  protected  from  dirt  and 
mechanical  injury  by  a  movable  hood  mounted  on  a  screw-thread 

'      18 


274 


ELECTRICAL  MEASUREMENTS 


of  the  same  pitch  as  the  winding  on  the  cylinder.  The  slider, 
which  is  always  in  contact  with  the  wire,  is  carried  by  the  hood, 
which  at  its  lower  edge  has  100  graduations;  fractions  of  a  turn 
can  then  be  read.  The  whole  turns  correspond  to  the  divisions 
on  the  vertical  scale  seen  at  the  front  in  the  upper  figure. 


-Ba. 


FIG.  156. — Leeds  and  Northrup  potentiometer. 

The  resistance  of  each  of  the  15  coils  which  are  in  series  witl 
the  slide  wire,  shown  between  D  and  A,  is  5  ohms.  The  standard 
potentiometer  current  is  J^o  amp.,  thus  making  the  drop  in 
each  coil  and  in  the  slide  wire  0.1  volt  and  the  total  drop  from 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    275 

B  to  A,  1.61  volts.  One  division  on  the  vertical  scale,  corre- 
sponding to  one  turn,  is  therefore  equivalent  to  0.01  volt,  and 
one  division  on  the  hood  to  0.0001  volt. 

The  instrument  is  designed  for  use  with  the  commercial  Weston 
cell,  which  has  no  appreciable  temperature  coefficient,  so  no 
temperature  adjustment  is  provided.  Such  cells  may,  however, 
differ  from  one  another  slightly  in  e.m.f.  (a  few  ten  thousandths 
of  a  volt),  and  each  is  accompanied  by  a  certificate  giving  its 
true  voltage.  In  order  that  the  instrument  may  be  conveniently 
used  with  different  cells,  the  rheostat  between  0  and  A  is  pro- 
vided. The  standard  cell  is  connected  between  the  movable 
arm  T  and  the  point  0^.5.  The  resistance  of  each  coil  of  OA  is 
0.005  ohm;  so  with  the  standard  current  of  ^o  amp.  flowing, 
the  drop  through  each  is  0.0001  volt.  There  are  19  of  these 
coils;  consequently,  cells  of  e.m.fs.  from  1.0170  to  1.0189  volts 
can  be  used,  the  arm  T  being  set  to  correspond  to  the  particular 
cell  used. 

By  means  of  a  double-throw  switch  the  galvanometer  may  be 
quickly  transferred  from  the  standard-cell  circuit  to  that  marked 
E.M.F;  as  the  two  circuits  are  entirely  distinct,  no  resetting  of  the 
instrument  is  necessary  when  checking  the  potentiometer  current. 
This  is  a  very  great  convenience. 

The  process  of  making  a  measurement  is  to  set  the  double- 
throw  switch  on  the  point  marked  "  Standard  Cell,"  and  vary  the 
rheostat  to  get  zero  deflection;  this  adjusts  the  potentiometer 
current  to  its  standard  value.  Then  throw  the  switch  to 
" E.M.F."  and  balance,  using  the  voltage  slides  without  altering 
the  rheostats,  and  read  off  V  directly  in  volts.  To  check  the 
potentiometer  current,  simply  throw  the  switch  to  "  Standard 
Cell"  and  press  the  key.  No  resetting  is  necessary. 

For  satisfactory  action  it  is  necessary  to  apply  a  little  vaseline 
to  the  slide  wire  occasionally. 

Low-scale  Arrangement. — If  the  current  through  BA  be  re- 
duced to  J^oo  amp.,  the  drop  through  each  coil  and  through  the 
slide  wire  becomes  }>{QQ  volt,  and  the  entire  range  of  the  potenti- 
ometer is  0.16  volt.  By  removing  the  plug  at  K  from  socket  1 
to  socket  0.1  the  resistance  OB  is  shunted  by  S,  which  is  of  such 
a  value  that  one-tenth  the  total  current  flows  through  OB. 


276 


ELECTRICAL  MEASUREMENTS 


The  resistance  K  is  so  adjusted  that  this  total  current  is  kept  at 
0.02  amp. 

In  using  any  form  of  potentiometer  it  is  absolutely  necessary 
to  check  the  potentiometer  current  before  taking  a  reading. 

Wolff  Potentiometer. — Referring  to  Fig.  157,  the  battery 
current  from  B  flows  through  all  the  coils  marked  X 100,  then  to 


FIG.  157. — Wolff  potentiometer. 

the  lower  group  marked  XO.l  where  it  traverses  the  coils  to  the 
left  of  the  contact  D  and  on  to  the  group  XI,  traversing  the  coils 
to  the  left  of  the  contact  E,  thence  to  the  coils  to  the  left  of  the 
contact  F  in  the  group  XlO,  and  on  through  all  the  coils  in  the 
group  X  1,000. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    277 

The  function  of  the  upper  sets  of  coils  in  the  groups  marked 
XlO,  Xl  and  XO.l,  which  are  connected  in  series  with  those  in 
the  lower  or  measuring  sets,  is  to  maintain  the  potentiometer 
current  at  a  fixed  value  irrespective  of  the  position  of  the  con- 
tacts D,  E,  F.  The  contacts  on  the  upper  and  lower  sets  of 
these  resistances  are  rigidly  connected  so  that  if  a  coil  is  removed 
from  the  lower  set  an  equal  coil  is  added  in  the  upper  set. 

When  the  switch  K  is  on  X,  the  derived  circuit  containing  the 
unknown  P.D.  is  connected  between  A  and  C  via  the  galva- 
nometer. By  manipulating  the  switches  the  resistance  between 
A  and  C  may  be  varied  from  0  to  18,999.9  so  if  the  current  be  kept 
constant  at  0.0001  amp.,  any  P.D.  between  0  and  1.89999  volts 
may  be  balanced. 

The  standard-cell  circuit  is  connected  between  the  eighth  and 
ninth  coils  in  group  X  1,000  and  the  contact  at  H ;  by  moving  this 
contact  the  resistance  between  the  terminals  of  the  standard- 
cell  circuit  may  be  varied  from  10,190  ohms  to  10,200  ohms  in 
1-ohm  steps.  The  instrument  may  thus  be  adjusted  so  that 
standard  cells  having  e.m.fs.  from  1.0190  to  1.0200  volts  may  be 
employed.  To  check  the  potentiometer  current  it  is  necessary 
merely  to  throw  the  switch  K  to  the  position  marked  TV  and 
to  depress  the  key. 

The  instrument  is  also  made  in  a  low-resistance  form  (14J^ 
ohms)  which  is  suitable  for  thermo-electromotive  force  determi- 
nations such  as  are  necessary  in  pyrometry. 

The  Brooks  Deflection  Potentiometer9. — The  potentiometers 
thus  far  described  are  read  by  the  null  method,  an  exact  balance 
being  obtained  between  the  potential  difference  in  the  instru- 
ment, due  to  the  potentiometer  current,  and  the  potential 
difference  to  be  measured.  The  objection  to  this  method,  is 
that  while  it  gives  results  of  the  highest  precision,  the  P.D. 
to  be  measured  must  be  steady,  and  repeated  trials  have  to  be 
made  before  the  balance  point  is  obtained.  When  the  unknown 
potential  difference  is  not  steady,  many  trials  must  be  made 
before  the  null  point  is  hit  upon  by  mere  chance,  and  the  ex- 
penditure of  time  and  patience  becomes  so  great  as  to  be  almost 
prohibitive  in  much  commercial  work. 

In  the  case  of  a  large  electrical  engineering  laboratory,  where 
many  instruments  must  be  checked  and  kept  in  adjustment,  it 


278 


ELECTRICAL  MEASUREMENTS 


is  imperative  that  the  work  be  done  with  great  speed,  combined 
with  the  accuracy  necessary  in  engineering  work. 

The  Brooks  potentiometer  was  designed  with  this  in  mind. 
By  it,  results  may  be  obtained  even  though  the  P.D.  under 
measurement  is  not  perfectly  steady.  In  this  instrument  no 


FIG.  158. — Brooks  deflectional  potentiometer. 

attempt  is  made  to  obtain  an  exact  balance;  the  slides  are  set 
so  near  to  the  null  point  that  the  galvanometer  deflection  is 
small.  The  galvanometer  is  so  graduated  that  it  gives  the 

amount  that  must  be  added 
to  the  reading  of  the  slides  in 
order  to  obtain  the  unknown 
P.D. 

That     certain     conditions 
must  be  fulfilled  may  be  seen 
from  the  following  discussion. 
In  general  the  potentiom- 
eter is  used: — 


FIG.  159. — Diagram  for  Brooks  deflec- 
tional potentiometer,  Case  I. 


I.  To   determine  potential 
differences  which  are  within 
the  normal  range  of  the  instrument. 

II.  To  determine,  by  the  use  of  a  volt  box,  potential  differences 
which  are  above  the  normal  range  of  the  instrument. 

III.  To  measure  currents  by  the  use  of  shunts. 
CASE  I.     DIRECT  MEASUREMENT  OF  P.D. 

A  storage  cell  is  used  at  e  (Fig.  159)  so  its  resistance  may  be 
neglected. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    279 

RG  is  the  resistance  of  the  galvanometer  plus  any  resistance 
placed  directly  in  series  with  the  instrument. 
The  mesh  equations  are: 

IG(EG  +  rO  -  yri  -  P.D.  =  0; 
y(ri  +  7*2  +  Bh)  -  IGrl  +  e  =  0. 


PD 


.     ,  +  r2  +  Bh 

K     ,. 

h 


i  +  7*2  +  Bh 

The  standard  potentiometer  current  when  it  has  been  adjusted, 
as  in  the  ordinary  potentiometer,  by  bringing  the  galvanometer 

/> 

to  zero  with  the  standard  cell  in  circuit,  is  —  —  --      p   •  there- 
fore -  —  HT-  is  the  graduation  marked  on  the  slides  of  the 

7*1  T-  ?*2  T~    -ft-ft 

instrument. 

If  the  null  method  be  employed, 


=  P-D-  =  reading  on  slides- 


The  instrument  being  in  exact  balance,  suppose  that  the  applied 
potential  difference,  P.D.,  is  increased  by  a  small  amount 
5[P.DJ,  so  that  it  becomes  P.D.  +  6[P.D.],  the  slides  being 
kept  as  they  were.  A  current  will  now  flow  through  the  galva- 
nometer and  its  value  will  be 

r  <[P.D.l 

+_Kh)_  (14) 


**G       I  I  I        DI, 

7*i  -\-  7*2  +  Hrl 

This  shows  that  in  measuring  any  potential  difference,  the  major 
portion  of  it  may  be  read  from  the  slides  as  usual,  and  to  this 

may  be  added  the  voltage  IO(RG  +  -  ~DT:)  m  order  to 

7*1  -f-  7*2  -\-  tin/ 

obtain  the  total  value. 

The  quantity  (RG  +  -  ~l>r)  *s  the  total  resistance  of 

\  7*]   •"["  7*2  ~T~  Kit/ 

the  galvanometer  circuit,  with  P.D.  and  e  short-circuited.     If 
this  resistance  be  kept  constant  for  all  positions  of  the  slides  and 


280 


ELECTRICAL  MEASUREMENTS 


the  adjusting  rheostat,  and  a  D' Arson val  galvanometer  be  used, 
the  galvanometer  scale  may  be  graduated  to  read  5[P.D.]  directly 
in  volts.  In  order  that  this  graduation,  as  a  .voltmeter,  may  be 
correct  for  all  three  of  the  cases  mentioned  above,  the  resistance 
of  the  galvanometer  circuit  must  always  be  kept  the  same, 
irrespective  of  the  use  to  which  the  potentiometer  is  put.  This 
is  the  cardinal  point  in  the  design  of  the  deflection  potenti- 
ometer, and  is  attained  by  an  ingenious  arrangement  of  coils 
and  switches. 

CASE  II.     POTENTIAL  DIFFERENCE  BY  USE  OF  VOLT  Box 


P.D. 


. R_ 

n 


Rh 

•AAA/W-- 


FIG.  160.  —  Diagram  for  Brooks  deflectional  potentiometer  Case  II. 
The  mesh  equations  are: 


xR  -  IG~  -  P.D.  =  0; 


R 


R 


y(ri  +  r2  +  Rh)  -  IGr,  +  e  =  0. 
P.D.  &n 


.'.    Io 


n 


+  r2  +  m 


Rh) 


If  the  slides  be  set  so  that  IG  is  zero,  then 
cri  P.D. 


If  now  the  potential  difference  be  increased  by  a  small  amount, 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    281 

S[P.D.],  the  slides  remaining  fixed,  a  current  will  flow  through 
the  galvanometer 

8[P.D.l 

/M 

Io  = 


R(n  -  1)  ri(r2  + 

n2  ^  +  r!  +  r2  +  /ta 

The  total  potential  difference  is,  therefore,  n  times  the  sum  of  the 
reading  of  the  slides  and  the  reading  of  the  galvanometer  in 
volts,  provided  the  coils  be  so  arranged  that 

J) 

Ko+ 


is  a  constant  for  all  settings  of  the  slides,  and  the  galvanometer 
has  been  calibrated  as  a  voltmeter  with  this  resistance.  The 
expression  in  parenthesis  is  the  total  resistance  of  the  galva- 
nometer circuit  when  e  and  the  volt  box  are  short-circuited. 

CASE  III.     CURRENT  MEASUREMENT 


FIG.  161. — Diagram  for  Brooks  deflectional  potentiometer  Case  III. 

The  mesh  equations  are: 

I0(S  +  RG  +  ri)  -  yrt  -  IS  =  0; 
y(ri  +  r2  +  fife)  -  Ian  +  e  =  0. 

IS  -         -^ 


r2  +  Rh 

"          " 

o  +  KG  + 


r2  +  jRA 
If  the  current  be  increased  by  a  small  amount  d[I]  from  that 


282  ELECTRICAL  MEASUREMENTS 

necessary  for  an  exact  balance,  the  slides  remaining  fixed,  the 
galvanometer  current  will  be 

Io  =  - 

S  +  Ro 

8[I]S  =  la 


PI  -\-  7*2  ~\~  Rh 
or 

ri(r8  +  Rh) 


TI  +  r2  +  Rfc/ 

The  expression  in  parenthesis  is  the  resistance  of  the  galva- 
nometer circuit  with  e  short-circuited  and  the  main  current  cir- 
cuit open  beyond  the  shunt.  The  quantity  to  be  added  to  the 
reading  of  the  slides  before  dividing  by  S  is  seen  to  be  the 
galvanometer  reading  reduced  to  volts,  provided  the  switches 
and  coils  are  so  arranged  that 


I       • «W       I       „        I      „       I       r> i  / 
PI  +  ^2  +  ttn/ 

has  a  fixed  value. 

To  obtain  the  greatest  speed  of  working,  the  resistance  of  the 
galvanometer  circuit  should  be  such  that  the  galvanometer  is 
critically  damped.  The  free  period  of  the  instrument  should  be 
about  1  or  2  sec.  The  arrangement  of  the  potentiometer  is 
shown  diagrammatically  in  Fig.  162. 

To  assist  in  attaining  the  necessary  constant  resistance  in  the 
galvanometer  circuit,  the  rheostat  for  controlling  the  potenti- 
ometer current  is  arranged  in  two  parts,  r3  and  r6,  the  potenti- 
ometer wire  being  connected  to  the  slider  which  joins  the  two 
sections;  the  coils  are  so  chosen  that  the  parallel  resistance  of 
the  active  portions  of  r3  and  r6  is  fixed,  thus  keeping  the  rheostat 
resistance  between  A  and  B  (with  e  short-circuited)  constant. 
The  rheostat  marked  0.5 12  is  for  the  fine  adjustment  of  the  potenti- 
ometer current;  the  corresponding  ballast  coils  in  the  galva- 
nometer circuit  are  marked  0.3 12.  To  correct  for  changes  in  resist- 
ance due  to  displacing  the  contact  point  along  the  potentiometer 
wire,  the  ballast  resistance  r4  is  added,  the  coils  in  it  being  given 
the  proper  values.  As  some  of  the  coils  at  the  upper  and  lower 
ends  of  the  series  have  the  same  values,  the  number  of  coils  re- 
quired is  reduced  by  cross-connecting,  as  shown  in  the  lower 
figure.  The  volt  box  employed,  shown  in  Fig.  163,  has  ballast 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    283 

coils  at  C,  which  are  in  series  with  the  connection  to  the  potenti- 
ometer proper.     When  currents  are  measured,  ballast  coils  are 


P.D.- 


-AVWWWWVWWW^ 


AVM^AA/VW\AAA/VV\AAAAA/WV\AAAMA/ 

T  Slider 


-VV\AAAAAAA/W\/W\/\A^AAAV\AAA/WV\/WN 


THEORETICAL    DIAGRAM 


Std.Cell 


20.85  _n_          15x0.1_n_ 


DIAGRAM    OF   ACTUAL  CONNECTIONS 

FIG.  162.  —  Diagram  of  connections  of  Brooks  deflectional  potentiometer. 

also  used.     They  are  mounted  in  the  case  of  the  instrument,  and 
are  shown  at  C  in  Fig.  162. 


284 


ELECTRICAL  MEASUREMENTS 


It  is  obvious  that  a  deflection  potentiometer  must  be  used  with 
the  particular  volt  box  and  shunts  for  which  it  was  designed. 


QAAO^<>MOMOA<>^— I 

y.33  -r-  2.C7-n-  0.98-n.  0.10-n.  O.12.n-  0.08 -«- 


—  Q     Poteatiomctor    Q  -f 


FIG.  163. — Volt  box  for  Brooks  deflectional  potentiometer. 

The  "Thermokraftfrei"  Potentiometer10. — In  the  measure- 
ment of  small  potential  differences  such  as  those  of  thermo- 
couples a  low  resistance  potentiometer  is  used,  and  it  is  necessary 
to  eliminate  all  thermo-electric  disturbances  due  to  contact  of 
dissimiliar  materials  and  inequalities  of  temperature  in  the 
potentiometer  itself;  therefore  the  metal  employed  in  the  coils 
and  in  their  terminals  must  be  carefully  selected  with  this 
result  in  view.  For  the  same  reason,  the  design  should  be  such 
that  the  effect  of  thermo-electromotive  forces  introduced  by 
the  manipulation  of  the  necessary  sliding  contacts  and  switches 
will  be  reduced  to  a  minimum.  This  is  accomplished  in  the 
instrument  under  discussion,  which  includes  elements  of  design 
due  to  H.  Hausrath,  W.  P.  White  and  H.  -Diesselhorst.  The 
potentiometers  previously  discussed  have  been  series  arrange- 
ments, that  is,  the  compensating  potential  difference  is  the  sum 
of  the  potential  differences  existing  between  the  terminals  of 
various  groups  of  coils  of  which  the  circuit  is  composed.  Haus- 
rath suggested  the  use  of  a  divided  circuit  in  place  of  coils  in 
series.  In  that  case  the  compensating  potential  difference  is 
due  to  the  difference  of  the  potential  drops  along  the  two  branches 
measured  from  the  point  where  the  current  enters  the  apparatus. 
Fig.  164  shows  in  diagram  the  arrangement  of  the  coils. 

The  potentiometer  current  is  kept  at  its  standard  value, 
0.001  amp.,  in  the  usual  manner  by  equating  the  drop  in  eg  to 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    285 

the  e.m.f.  of  the  standard  cell;  Rh  is  the  regulating  rheostat;  Si 
is  a  reversing  switch  in  the  main  circuit. 

The  current  entering  at  Tl  divides,  the  resistances  being  so 
arranged  that  ten-elevenths  of  the  total  current  flows  to  the  left 


FIG.   164. — Thermokraftfrei  potentiometer. 

and  one-eleventh  to  the  right.     The  design  is  such  that  these 

relative  values  are  maintained  for  all  positions  of  the  switches. 

Each  coil  in  the  decade  I  and  in  the  group  of  compensating 


286  ELECTRICAL  MEASUREMENTS 

coils  I'  has  a  resistance  of  1  ohm,  and  the  sliding  terminals 
TT  and  T\  are  mechanically  connected  so  that  if  Tt  is  shifted 
to  the  right,  T\  is  shifted  an  equal  number  of  coils  to  the  left. 
The  resistances  of  both  paths  between  the  terminals  T^  and 
T\  are  thus  kept  constant. 

As  all  the  coils  in  decades  II  and  III  and  all  the  compensating 
coils  in  II'  and  III'  are  alike,  the  resistances  of  both  the  left- 
and  the  right-hand  branches  of  the  circuit  are  independent  of 
the  positions  of  Tn  and  Tm. 

The  two  sliding  contacts  on  decades  IV  and  the  compensating 
coils  IV'  are  mechanically  connected  so  that  they  must  move 
together,  as  are  the  two  on  decade  Fand  its  compensating  coils  V. 
If  the  contact  in  decade  IV  is  set  on  a  terminal  having  a  certain 
number,  then  automatically  the  contact  in  group  IV'  is  set  on  the 
terminal  of  the  same  number,  and  similarly  with  V  and  V.  The 
group  of  coils  IV,  consists  of  a  1-ohm  coil  (  —  1.0  in  group  I), 
shunted  by  a  variable  resistance  which  consists  of  a  fixed  portion, 
81.64co,  and  a  variable  part  included  between  —  1  and  the  posi- 
tion of  the  sliding  contact.  The  coils  in  the  variable  portion 
of  IV  are 

Between  Ohms  Between  Ohms 

-landO  8.264  4  and  5  30.30 

Oandl  10.101  5  and  6  45.41 

1  and  2  12 . 626  6  and  7  75 . 80 

2  and  3  16.234  7  and  8  151.51    ' 

3  and  4  21.645  8  and  9  454.54 

9  and  10  « 

In  the  group  IV  the  order  is  reversed,  that  is,  the  coil  having 
a  resistance  of  8.264  ohms  is  between  contacts  9  and  10.  The 
resistances  are  given  these  particular  values  in  order  that, 
when  the  contact  in  IV  is  moved  one  number,  the  resistance 
between  Tl  and  Tu  may  always  be  altered  by  a  definite  amount, 
0.0011  ohm,  which  is  Koo  of  the  alteration  which  would  be 
obtained  by  moving  Tn  one  number.  For  instance,  if  the  decade 
contact  is  on  number  4,  the  resistance  of  group  IV  is 

0050.51 
Hlv       1  +  150.51 
When  it  is  set  on  number  5,  this  becomes 


Rlv   =  H^ZZ  "  =  0.9890 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    287 

The  difference  of  these  two  values  is  0.0011  ohm  while  the  value 
of  a  single  step  in  IT  is  0.11  ohm. 
The  minimum  value  of  Rlv  is 

1  X  89.904 
1  +  89.904 
so  the  general  value  is 

Rlv  =  0.9890  +  0.0011  X  nlv 

where  nlv  is  the  number  of  the  contact  on  dial  IV. 
Similarly  the  general  value  of  Rlv>  is 

Rlv>  =  0.9989  -  0.0011  X  nlv/. 

In  decade  V  the  coil  of  8.264  ohms  is  between  contacts  9  and  10; 
in  the  group  of  compensating  coils,  V,  it  is  between  —  1  and  0, 
so,  in  general, 

Rv   =  0.9989  -  0.001  lwv 

Rv>  =  0.9890  +  0.001  Irv 

The  coils  b,  c,  d,  have  such  values  that  taken  in  conjunction  with 
the  other  resistances,  they  divide  the  current  flowing  in  at  Tl 
in  the  ratio  10  to  1. 

The  voltage  between  Tn  and  Tul  is  the  difference  of  the  ohmic 
drops  measured  from  T1}  so  for  any  setting  (potentiometer  current 
0.001  amp.) 


P.D.  = 


X  0.001  [n,  X  1  +  0.9890  +  0.001  lnlv  • 

+  0.11089  +  0.11(wH  +  1)] 
-  ~  X  0.001  [(10  -  n,)l  +  0.9989  -  0.0011nv 

+  0.11(10  -nni)] 

,   Wn       nni         nlv  nv    ~\ 

1  [n,  +  rQ+  m  +  j-ggg  +  jg-^gj. 

Therefore  when  the  dials  are  properly  graduated  the  unknown 
P.D.  is  measured  by  the  sum  of  the  dial  readings,  as  in  the  usual 
instruments. 

A  study  of  the  network  shows  that  if  the  battery  circuit  is 
open,  the  resistance  between  the  galvanometer  terminals  +X 


288  ELECTRICAL  MEASUREMENTS 

and  —X  is,  to  a  good  degree  of  approximation,  14.35  ohms,  and 
when  the  battery  circuit  is  closed  through  a  series  resistance,  B, 
which  is  external  to  the  potentiometer  the  resistance  becomes, 
using  a  second  approximation, 

14.35  -  _ 


where  R  is  the  resistance  of  the  potentiometer  between  Tl  and 
Tj  with  the  galvanometer  circuit  open. 

The  resistance  of  the  right-hand  path  between  Tl  and  T\ 
is  990  ohms;  that  of  the  left-hand  path,  99  ohms;  the  resistance 
of  the  whole  apparatus  is  therefore  R  =  90  ohms. 

If  a  storage  cell  is  used  and  the  potentiometer  current  is 
0.001  amp.,  R  +  B  must  be  approximately  2,000co;  therefore, 
the  maximum  variation  in  the  resistance  of  the  galvanometer 
circuit  will  be  only  0.05  ohm  or  about  0.3  per  cent.  This  con- 
stancy of  the  resistance  allows  one  to  obtain  the  last  figure  in  the 
P.D.  under  measurement,  by  the  deflection  method,  the  reading 
of  the  last  decade,  n?,  being  kept  at  zero.  By  properly  setting 
up  the  apparatus,  the  full  reading  of  the  last  decade,  nv  =  10, 
may  be  made  to  correspond  to  1,  10,  or  100  divisions  on  the 
galvanometer  scale  and  the  necessity  for  exact  balancing  may 
thus  be  obviated.  Where  the  P.D.  to  be  measured  is  fluctuating 
slightly,  this  is  a  decided  advantage  (see  page  277,'  "Brooks 
Deflection  Potentiometer"). 

Another  advantage,  if  a  moving-coil  galvanometer  is  used,  is 
that  the  damping  remains  constant,  irrespective  of  the  setting 
of  the  potentiometer. 

Effect  of  Thermo  -electromotive  Forces.  —  The  magnitude  of 
the  e.m.f  .  set  up  by  manipulating  any  switch  is  less  than  10~6  of  a 
volt. 

Any  e.m.fs.  arising  from  manipulating  /  and  1'  are  added  to 
the  battery  e.m.f.  (2  volts)  and  will  be  negligible.  The  effect 
of  a  thermo-electromotive  force  of  magnitude  e,  due  to  moving 
contact  II,  will  be  very  small. 

Referring  to  Fig.  165,  by  KirchofFs  laws  the  current  in  the  left- 
hand  branch,  if  I  is  the  total  battery  current  coming  to  the 
potentiometer,  is 

I  (0  +  5)  +  e 
IL   " 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    289 

and  in  the  right-hand  branch 

I(a  +  7)  +  6 


Therefore,  the  change  in  the  P.D.  between  the  terminals  +  X 
and  —X  due  to  +  e  will  be 


The  maximum  value  of  7  +  6  is  14.42  ohms  and  the  value  of 
a  +  /3  +  7  +  Sis  1,089  ohms,  so 

-  =  «  X  0.013 


a  7 

.'.  the  error  introduced  is  only  1.3  per  cent  of  e. 


FIG.   165. — Pertaining  to  effe'ct  of  thermal  e.m.f.  in  thermokraftfrei 
potentiometer. 

Similar  considerations  show  that  the  error  introduced  by 
manipulating  IV  and  V  is  only  about  1.2  per  cent,  of  e.  These 
errors  having  been  reduced  to  negligible  amounts,  the  apparatus 
is  said  to  be  free  from  thermo-electromotive  forces. 

Application  of  the  Potentiometer  to  Alternating-current 
Measurements. — The  principle  involved  in  the  potentiometer 
was  applied  to  alternating-current  measurements  many  years  ago, 
but  at  that  time  the  necessary  adjunct  of  a  convenient  phase- 
shifting  device  had  not  been  developed  by  Drysdale,  and  recourse 
was  had  to  an  arrangement  of  two  small  dynamos  on  the  same 
shaft,  one  of  which  could  be  displaced  in  phase  with  reference 
to  the  other.  The  arrangement,  while  satisfactory  in  many  ways, 
is  much  less  convenient  and  more  costly  than  the  phase-shaft- 
ing transformer  now  used.  The  development  of  the  alternating- 

19 


290 


ELECTRICAL  MEASUREMENTS 


current  potentiometer  as  a  distinct  instrument  is  due  to 
C.  V.  Drysdale,  whose  instrument  is  shown  diagrammatically 
in  Fig.  167. 

In  applying  the  potentiometer  principle  to  alternating-current 
measurements  it  is  obvious  that  to  balance  two  potential  differ- 
ences at  every  instant,  they  must  be  of  the  same  frequency,  the 
same  wave  form,  and  in  the  same  time  phase.  The  first  two 
conditions  demand  that  the  potentiometer  current  be  derived, 
through  a  suitable  transformer,  from  the  same  source  as  the  cur- 
rent to  be  measured.  The  third  implies  the  use  of  some  form  of 

phase-shifting  device.  In  addition 
there  must  be  some  means  of  insur- 
ing that  the  potentiometer  current, 
when  it  is  alternating,  is  of  such  a 
magnitude  that  the  r.m.s.  value  of 
the  potential  difference  between  the 
terminals  of  each  of  the  coils  of  the 
instrument  is  given  by  the  poten- 
tiometer scale.  As  the  coils  are 
wound  non-inductively,  this  may  be 

FIG.  166.— Theoretical  diagram  accomplished   if   the   potentiometer 
for  Drysdale  phase  shifter. 

current  be  measured  by  an  electro- 
dynamometer  of  the  astatic  form.  Such  an  instrument  gives 
r.m.s.  values  and  is  equally  accurate'  on  direct  and  alternating 
current  circuits;  therefore  it  is  very  readily  calibrated. 

The  Drysdale  Phase  Shifter. — The  principle  involved  in  the 
Drysdale  phase-shifting  transformer  may  be  illustrated  by  the 
following  ideal  arrangement  of  the  apparatus  (Fig.  166).  The 
two  sets  of  coils  are  of  equal  magnetic  strength  and  may  have 
their  axes  at  right  angles,  in  which  case  they  are  energized  by 
currents  in  quadrature,  as  from  the  two  phases  of  a  two-phase 
circuit.  The  secondary  is  so  mounted  that  it  may  be  turned  by 
hand  and  clamped  in  position;  thus  6  may  be  given  any  desired 
value.  Let  the  coils  in  phase  2  be  traversed  by  a  current  /  sin  cot, 
and  the  coils  in  phase  1  by  a  current  90°  out  of  phase  with  the 
first,  or  I  cos  ut.  The  rectangular  components  of  the  resultant 
field  at  the  center  are 

x  =  H  sin  ut ;         .• 

y  =  H  cos  wt. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    291 

The  resultant  is 

R  =  \/x2  +  y2  =  H  Vsiri2  ut  +  cos2  ut  =  H,  a  constant. 

At  any  instant  the  tangent  of  the  inclination  of  this  resultant 
to  the  vertical  axis  is  -; 

y 

/y» 

tan  7  =  -  =  tan  ut; 

& 

:.  7  =  «t. 

Therefore  the  resultant  field  at  the  center  is  of  constant  magni- 
tude and  revolves  with  a  constant  angular  velocity. 

The  flux  threading  the  secondary  coil  is  proportional  to  cos 
(ut  —  6)  and  the  induced  e.m.f.  to  sin  (cot  —  6),  so  the  time- 
phase  displacement  of  the  induced  e.m.f.  is  equal  to  the  angular 
displacement  of  the  secondary  from  its  zero  position. 

In  the  actual  construction  of  the  phase  shifter  the  four  sta- 
tionary coils  are  replaced  by  stator  windings  of  the  induction- 
motor  type;  the  secondary  is  wound  on  an  iron  core.  As  built 
by  some  makers  the  apparatus  has  the  fault,  serious  in  some 
methods  of  measurement,  that  change  of  phase  is  accompanied 
by  an  alteration  of  secondary  e.m.f.  This  is  obviated  in  Dr 
Drysdale's  own  design  by  a  proper  arrangement  of  the  windings. 
If  the  currents  supplied  to  the  phase  shifter  are  not  sinusoidal 
the  wave  form  in  the  secondary  will  depend  on  the  value  of  6. 
The  device  may  be  wound  so  as  to  operate  on  either  two-  or 
three-phase  circuits,  or  it  may  be  arranged  to  be  operated  on  a 
single-phase  circuit  by  means  of  a  phase-splitting  device.  The 
phase*  shifter  or  its  equivalent  is  a  necessary  adjunct  of  the 
alternating-current  potentiometer. 

The  Drysdale-Tinsley  Alternating-current  Potentiometer. — 
The  Drysdale-Tinsley  alternating-current  potentiometer  is  shown 
diagrammatically  in  Fig.  167.  It  consists  of  a  regular  Tinsley 
potentiometer,  such  as  is  used  for  direct-current  work  (included  in 
the  dotted  rectangle) ,  supplemented  by  the  electrodynamometer 
necessary  for  the  measurement  of  the  potentiometer  current; 
a  selector  switch,  for  quickly  transferring  the  instrument  from 
one  set  of  terminals  to  another;  a  connection  bo  ard,  by  which 


292 


ELECTRICAL  MEASUREMENTS 


the  potentiometer  is  attached  to  the  outside  circuits;  a  change- 
over switch,  for  quickly  substituting  alternating  for  direct  cur- 
rent; and  the  phase  shifter;  this  last  device  is  best  operated  from  a 
single-phase  circuit  by  means  of  a  phase-splitting  condenser  and 
resistance.  This  arrangement  is  best  because  any  single-phase 
supply,  of  good  wave  form,  can  be  used  and  all  doubt  as  to  the 
exact  quadrature  of  the  two  phases  eliminated. 

The  phases  can  be  adjusted  to  within  0°.l,  the  procedure  being 
as  follows :  Join  the  100- volt  supply  to  the  two  terminals  m'arked 
Phase  1  on  the  phase-shifting  transformer.  The  condenser  and 


cffi      Amt       ",:&      Am°p.      v^fc     [fiat.    [Rotor  Galv.Vib.Galv. 
6          O          Q          O          O 

1 


FIG.  167. — Diagram  for  Drysdale-Tinsley  alternating-  and  direct-current 

potentiometer. 


resistance,  in  series  with  the  terminals  marked  Phase  2,  are  also 
connected  across  the  100-volt  supply.  The  secondary  is  then 
turned  by  the  tangent  screw  until  the  pointer  marked  AXIS,  is 
at  0°  on  the  dial.  By  means  of  the  rheostat  of  the  potenti- 
ometer, the  current  is  adjusted  until  the  dynamometer  reads 
exactly  50.  Then  the  tangent  screw  is  turned  until  the  AXIS 
pointer  is  at  45°  leading.  If  the  dynamometer  reads  higher  or 
lower  than  50  the  capacity  is  altered  until  the  reading  is  correct. 
The  AXIS  pointer  is  then  turned  to  90°  and  the  resistance  altered 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    293 

until  50  is  again  registered.  After  this  the  dynamometer  should 
remain  exactly  at  50,  while  the  secondary  is  turned  through 
180°;  if  it  does  not  so  remain  the  process  is  repeated  until  it 
does  remain  at  50  for  all  positions  of  the  secondary. 

In  measuring  currents  or  e.m.fs.  it  is  not  ne'cessary  to  split  the 
phase  with  great  accuracy,  although  it  is  more  convenient  to  do 
so ;  but  the  utmost  care  must  be  taken  in  doing  this  when  vector 
diagrams  are  being  constructed  or  when  an  accurate  knowledge 
of  phase  angles  is  required. 

Above  all  things,  it  is  necessary  that  the  supply  voltage  and 
frequency  remain  perfectly  steady. 

After  the  adjustment  of  the  phase  splitter,  the  first  step  in 
using  the  instrument  is  to  calibrate  the  electrodynamometer  at 
the  reading  corresponding  to  the  standard  potentiometer  current. 
To  do  this  the  battery  is  used  as  a  source  and  the  adjustment 
made  as  with  the  ordinary  potentiometer.  The  Tinsley  instru- 
ment has  no  separate  standard-cell  tap,  so  it  is  necessary  to  set 
the  slides  at  the  voltage  of  the  cell  and  then  adjust  the  rheostat; 
this  process  must  be  repeated  whenever  the  standard  potentiom- 
eter current  is  checked.  When  the  galvanometer  is  in  balance 
the  reading  of  the  dynamometer  is  taken;  if  the  instrument  is 
not  astatic,  reversed  readings  must  be  taken  and  the  two  results 
averaged.  By  means  of  the  change-over  switch,  alternating  is 
substituted  for  direct  current  and  the  reading  brought  to  the  same 
value  and  held  there.  Then  the  graduation  in  volts  on  the 
potentiometer  scale  gives  r.m.s.  values  of  the  P.D.  First 
the  phase  of  the  potentiometer  current  is  roughly  adjusted;  then 
the  unknown  P.D.  is  balanced  as  nearly  as  possible  by  the  po- 
tentiometer slides.  The  balance  is  then  improved  by  shifting 
the  phase  of  the  potentiometer  current  and  still  further  im- 
proved by  resetting  the  slides;  thus,  by  a  process  of  double 
adjustment,  the  vibration  galvanometer  which  is  used  as  the 
detector  is  brought  to  rest.  As  the  vibration  galvanometer  is 
a  tuned  instrument  which  responds  freely  to  currents  of  only 
one  frequency,  the  periodicity  of  the  supply  current  must  be  kept 
constant  if  the  sensitivity  of  the  potentiometer  is  to  be  main- 
tained. With  any  potentiometer  the  deflection  of  the  detector 
is  dependent  on  the  difference  of  the  two  potential  differences 
which  are  being  balanced.  As  the  vibration  galvanometer  which 


294  ELECTRICAL  MEASUREMENTS 

is  used  as  a  detector  is  tuned  to  the  fundamental  frequency  of 
the  circuit  a  balance  indicates  that  the  values  of  the  funda- 
mentals and  not  the  mean  square  values  of  the  P.D.'s  are  equal. 
If  the  wave  forms  are  very  bad  the  vibration  galvanometer  may 
be  forced  to  vibrate  in  other  than  its  natural  period,  in  which  case 
an  exact  balance  cannot  be  obtained.  It  is  seen  that  sinusoidal 
currents  are  necessary  for  the  successful  operation  of  the  alter- 
nating-current potentiometer. 


STANDARD  CELLS 

In  order  to  realize  and  maintain  the  international  volt  in  such 
a  manner  that  it  will  be  a  practical  unit,  easily  applied  for  pur- 
poses of  measurement,  recourse  must  be  had  to  some  form  of 
galvanic  cell.  Reference  to  the  section  on  the  legal  definitions 
of  the  electrical  units  will  show  that  in  the  Act  of  Congress 
approved  July  12,  1894,  the  Clark  normal  cell  was  mentioned, 
and  this  act  is  still  in  force.  At  that  time  this  cell  was  the  only 
one  that  had  been  carefully  investigated  and  shown  to  have  the 
necessary  characteristics  of  reproducibility  and  permanence. 
It  has  since  been  shown  that  the  Weston  normal  cell  is  very 
nearly  as  reproducible  and  more  permanent;  it  possesses  the 
practical  advantage  of  having  a  much  smaller  temperature 
coefficient,  only  about  one-twentieth  of  that  of  the  Clark  cell. 

The  Weston  normal  cell  was  recommended  by  the  London 
Conference  on  Electrical  Units  and  Standards,  1908,  for  use  in 
voltage  and  current  measurements  and  was  adopted  by  the 
Bureau  of  Standards  as  the  working  standard  for  the  United 
States  on  Jan.  1,  191 1.14 

The  Clark  Cell. — This  cell,  the  invention  of  Latimer  Clark, 
was  described  by  him  and  recommended  as  a  standard  of  electro- 
motive force  in  a  paper  read  before  the  Royal  Society.12 
The  cell  consists  of  a  zinc  electrode  in  a  neutral,  saturated  zinc 
sulphate  solution  opposed  to  a  mercury  electrode  covered  with  a 
paste  consisting  of  mercurous  sulphate  and  zinc  sulphate  in 
saturated  zinc  sulphate  solution  and  containing  finely  divided 
mercury.  The  function  of  the  mercurous  sulphate  is  that  of  a 
depolarizer. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    295 

Board  of  Trade  Cell. — Little  careful  work  was  done  on  the 
Clark  cell  until  1885,  when  Lord  Rayleigh  investigated  a  form  of 
cell  practically  similar  to  that  shown  in  Fig.  168,  which  is  the 
Board  of  Trade  cell  of  1894.  Rayleigh  found  that  the  e.m.f.  of 
the  cell  at  any  temperature  could  be  expressed  by  the  formula, 

Eta  =  #15o(l  -  0.00077[Z°  -  15°]); 

and  gave  1.434  as  the  value  of  the  e.m.f.  at  15°;  subsequent 
investigation  has  shown  that  this  figure  is  too  high  by  nearly 
0.1  per  cent. 


-Marine  Glue 
Zinc  Rod 


41-Air  Bubble 

Sulphate 

Solution 
nc  Sulphate 
-r...  Crystals 

:^£    JPaste 

•^    "^Mercurous  Sulphate 
^     [Zinc  Sulphate 


!?S-j-Zi 


Mercury 


FIG.  168.— Board  of  Trade 
,  standard  Clark  cell,  1894. 


Marine  Glue 


rk 


Zinc  Rod 

Zinc  Sulphate 

Solution 

Saturated  at  O°C. 

.Cork 

Paste 

Mercurous  Sulphate 

Zinc  Sulphate 

Mercury 


FIG.  169 .— Carhart-Clark 
standard  cell.  Used  as  a  work- 
ing standard  before  the  intro- 
duction of  the  Weston  cell. 


Rayleigh  showed  that  variations  in  the  e.m.f.  were  due  to  im- 
purities in  the  materials,  and,  in  this  form  of  cell,  to  the  fact  that 
the  zinc  was  so  placed  that  it  was  not  covered  by  zinc  sulphate 
solution  of  uniform  density ;  this  greatly  retarded  the  response  of 
the  e.m.f.  to  a  change  of  temperature.  The  first  effect  of  a 
decrease  in  temperature  would  be  to  cause  crystallization;  this 
requires  time,  consequently  the  density  in  the  neighborhood  of 
the  crystals  lags  behind  the  temperature  change  and  a  still 
longer  time  must  elapse  before  the  solution  becomes  uniform  by 
diffusion.  This  accounts  for  the  lack  of  concordance  in  the  early 
values  of  the  temperature  coefficient.  This  lag  in  the  e.m.f. 
becomes  greater  as  the  cells  grow  older,  especially  if  they  are 


296 


ELECTRICAL  MEASUREMENTS 


kept  at  a  uniform  temperature  and  not  disturbed,  for  then  the 

zinc  sulphate  crystals  gradually 
unite  in  a  compact  mass. 

The  H  Cell.— A  much  more 
satisfactory  cell,  designed  by 
Lord  Rayleigh  and  known  as 
the  H  form,  is  shown  in  Fig. 
170  which  shows  an  hermetically 
sealed  cell;  the  zinc  is  used  in 
the  form  of  an  amalgam,  and 
the  platinum  terminals  are 
amalgamated  to  prevent  acci- 
dental contact  with  the  elec- 
trolyte. 

This  cellhas  been  thoroughly 
FIG.  170.— H  form  of  Clark  ,.    ,    ,       T,  ,  , 

standard  cell.  studied  by  Kahle,  and  later  in 

this     country    by     Wolff     and 
Waters.     The  latest  results  show  that  with  skilled  manipulation 


Air  Bubble 


Zinc  Sulphate 
Crystals 

Paste 

Mercurous 

Sulphate 

Zinc  Sulphate 

Mercury 


Zinc  Sulphate 

Solution 
Saturated 


Zinc  Sulphate 
Crystals 


Amalgam 
10*  Zinc 


FIG.  171.— Kahle  H  form  of  Clark  cell, 
it  is  reproducible  to  within  a  few  parts  in  100,000.     This  cell  19 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    297 

much  more  permanent  than  the  Board  of  Trade  form  and  has 
a  much  smaller  lag  error — only  about  one-fourth  as  great.  Local 
actions  arising  from  differences  in  density  are  also  avoided. 

The  form  of  cell  mentioned  in  the  specifications  prepared  by 
the  National  Academy  of  Sciences  in  compliance  with  the  Act 
of  Congress  dated  July  12,  1894,  was  developed  at  the  Reich- 
sanstalt,  by  Kahle,  and  is  shown  in  Fig.  171. 

The  value  of  the  e.m.f.  at  15°C.  stated  in  the  Act  of  1894  is 
1.434,  but  subsequent  investigation  has  shown  that  the  value 
really  is  1.4328  international  volts. 

The  H  form  of  Clark  cell  has  the  disadvantage  of  short  life, 
for  the  glass  is  likely  to  crack  where  the  platinum  electrode  is 
fused  in  at  the  amalgam  terminal.  N 

Materials  Used  in  Standard  Cells. — In  order  that  the  e.m.f.  of 
any  form  of  primary  standard  cell  may  accord  with  the  stated 
value,  great  care  must  be  exercised  in  the  preparation  of  the 
materials,  the  processes  for  which  have  been  carefully  worked 
out  by  Kahle  and  later  by  'Wolff  and  Waters.13 

Many  of  the  impurities  ordinarily  found  in  the  chemicals 
employed  have  but  a  small  effect  on  the  e.m.f.,  so  that  secondary 
standards  may  be  set  up  with  the  best  of  c.p.  materials,  except 
the  mercurous  sulphate,  which  must  be  specially  prepared.  Cells 
so  set  up  should  not  differ  by  more  than  0.01  per  cent,  from  those 
where  the  greatest  care  has  been  exercised  in  the  preparation  of 
the  materials. 

The  mercury,  if  badly  contaminated,  may  be  subjected  to  a 
preliminary  purification  by  electrolysis.  The  mercury  is  made 
the  anode,  a  piece  of  platinum  foil  the  cathode,  and  the  electro- 
lyte is  2  per  cent,  nitric  acid  in  water;  the  mercury  is  constantly 
stirred.  The  more  positive  metals  go  almost  completely  into 
solution  by  electrolysis;  the  less  positive  metals,  which  affect  the 
e.m.f.  but  little,  are  left  in  the  mercury,  which  is  then  distilled 
twice  in  a  current  of  air  at  greatly  reduced  pressure.  This 
oxidizes  the  remaining  impurities  which  distil  with  the  mercury; 
the  oxides  float  on  the  surface  and  are  removed  by  passing 
the  mercury  through  a  pinhole  in  a  filter  paper. 

The  zinc  is  distilled  at  reduced  pressure  to  remove  the  small 
amounts  of  cadmium,  lead,  iron,  and  arsenic,  which  are  the  usual 
impurities. 


298  ELECTRICAL  MEASUREMENTS 

The  zinc  sulphate  must  be  treated  to  remove  the  sulphates  of 
cadmium,  iron,  lead,  and  free  sulphuric  acid;  the  last  has  the 
greatest  effect  on  the  e.m.f.  and  gives  rise  to  the  formation  of 
gas  at  the  amalgam. 

The  purity  of  the  mercurous  sulphate  is  of  prime  importance; 
lack  of  purity  of  this  salt  is  the  chief  cause  of  variation  in  the 
e.m.f.  The  usual  impurities  are  basic  mercurous  sulphate,  basic 
mercuric  sulphate,  traces  of  mercuric  nitrate,  etc.,  according  to 
the  method  of  preparation.  This  salt  is  subject  to  the  action 
of  light  and  must  be  prepared  in  subdued  light  and  preserved 
in  the  dark  under  dilute  sulphuric  acid.  Great  care  must  be 
exercised  in  washing  it  before  use  to  free  it  from  sulphuric  acid, 
the  washing  being  done  with  absolute  alcohol,  which  in  turn  is 
removed  by  zinc  sulphate  solution. 

This  salt  may  be  made  by  a  number  of  methods,  all  of  which 
give  satisfactory  results,  the  best  one,  apparently,  being  an 
electrolytic  method  devised  by  Wolff  and  Waters.  The  mercury 
anode  is  at  the  bottom  of  a  tall  jar,  the  cathode  a  piece  of  plati- 
num foil  suspended  above  the  anode,  and  the  electrolyte  is 
dilute  sulphuric  acid.  The  mercury  is  violently  stirred  during 
the  passage  of  the  current  and  for  some  time  after  the  circuit  is 
broken. 

The  Weston  or  Cadmium  Cell.13— As  early  as  1884  Czapski 
called  attention  to  the  low  temperature  coefficients  of  cells  with 
cadmium  electrodes,  but  the  matter  was  forgotten  until  1892, 
when  attention  was  recalled  to  this  type  of  cell  by  Edward 
Weston.  The  cell  suggested  by  him  is  composed  of  cadmium 
in  cadmium  sulphate  solution  opposed  to  mercury  in  mercurous 
sulphate  paste.  The  particular  advantage  of  this  form  of  cell 
is  its  very  small  temperature  coefficient.  This  is  in  consequence 
of  the  fact  that  the  solubility  of  the  cadmium  salt  is  only  slightly 
influenced  by  the  temperature,  consequently  the  changes  in 
density  of  the  solution  are  very  small.  Also  the  temperature 
effects  on  the  two  limbs  of  the  cell  tend  toward  compensation. 
The  normal  form  of  this  cell  has  been  studied  at  the  Reichsan- 
stalt  by  Jaegar,  Kahle,  Wachsmuth,  and  Lindeck,  and  in  this 
country  by  Wolff  and  Waters.  The  cadmium  is  used  in  the 
form  of  an  amalgam  made  by  dissolving,  with  the  aid  of  heat, 
1  part  of  Kahlbaum's  best  cadmium  in  7  parts  of  mercury.  If 


MEASUREMENT -OF  POTENTIAL  DIFFERENCE    299 


necessary,  the  cadmium  may  be  purified  by  distillation  at  re- 
duced pressure. 

The  effect  of  variation  of  the  concentration  of  the  amalgam 
is  shown  in  Fig.  173,  which  gives  the  e.m.f s.  when  various 
amalgams  are  tested  against 
one  having  14.2  per  cent,  of 
cadmium,  the  electrolyte  being 
saturated  cadmium  sulphate 
solution.  Variable  results  were 
obtained  when  the  percentage 
of  cadmium  was  over  14.5  per 
cent.  Amalgamated  cadmium 
rods  also  gave  variable  results. 
Identical  results  (to  O'.OOOOl) 
were  given  by  amalgams  con- 
taining from  6  to  14.3  per  cent, 
of  cadmium. 

It    may   be    noted    that    the 
stability  of  the  amalgam  when  FlG-  172.— Weston  normal  standard 

cell 

subjected  to  variations  of  tem- 
perature is  influenced  by  its  composition;  irregularities  in  the 
behavior  of  the  cell  were  noticed  at  about  15°C.  At  first  it 
was  supposed  that  these  were  due  to  an  inversion  of  the  cad- 
mium sulphate,  similar  to  that  of  zinc  sulphate  at  39°,  but 
later  it  was  found  that  they  were  due 
to  the  amalgam,  and  were  obviated  by 
employing  a  12.5  per  cent,  in  place  of 
the  14.3  per  cent,  amalgam  at  first 
used. 

The  e.m.f.  at  20°  of  the  normal  cad- 
mium cell,  containing  saturated  solu- 
tion, is,  when  derived  from  the  inter- 
national ampere  and  the  international 
ohm,  1.01830  international  volts.14  Its 
e.m.f.  at  any  temperature,  t,  is 

Et  =  #20  -  0.0000406[*  -  20]  -  0.00000095[*  -  20] 2 
+  0.000000001  [t  -  20]3. 

The  advantages  of  the  cadmium  cell  are  low  temperature 


:ui  — 

Unste 
%  of  Cadmium^ 

£ 

,/ 

*         1 

0          1 

5 

/ 

,0?v 

FIG.  173.— Illustrating 
effect  of  strength  of  amal- 
gam in  the  cadmium  cell. 


300 


ELECTRICAL  MEASUREMENTS 


coefficient;  exceedingly  small  lag  error;  long  life,  due  to  freedom 
from  cracking  at  the  negative  electrode;  continuity  of  action, 
due  to  the  fact  that  gas  is  not  formed  at  the  negative  electrode. 

The  Weston  Secondary  Standard  Cell.— The  Weston  Instru- 
ment Co.  has  placed  on  the  market  the  convenient,  portable 
form  of  cadmium  cell  shown  in  Fig.  174.  The  solution  is  satu- 
rated at  4°C.,  and  therefore  does  not  contain  an  excess  of  cad- 
mium sulphate  crystals.  This  type  of  cell  is  to  be  used  between 
the  temperatures  of  4°  and  40°.  The  temperature  coefficient 
is  much  smaller  than  that  of  the  normal  cell  and  is  negligible  for 
any  ordinary  measurements;  each  cell  is  accompanied  by  a 
certificate  stating  its  e.m.f.  The  extreme  variation  among  145 


Mercurous  _ 
Sulphate  Paste 


Mercury          Cement 

FIG.  174. — Weston  secondary  standard  cell.     A  working  standard  of  elec- 
tromotive force. 

cells  of  this  type  was  found  to  be  0.0009  volt.  This  is  the  best 
form  of  secondary  standard  cell,  being  remarkably  permanent. 
The  e.m.f.  is  very  closely  1.0186  international  volts;  the  resistance 
about  200  ohms. 

Precaution  in  Using  Standard  Cells. — No  appreciable  current 
can  be  taken  from  a  standard  cell  without  alteration  of  its  e.m.f., 
due  to  polarization.  It  is  found  that  the  change  is  not  perma- 
nent, for  the  cell  gradually  recovers  its  original  e.m.f.;  the  cell  is 
unreliable  until  the  recovery  is  complete.  This  being  so,  stand- 
ard cells  are  used  only  in  compensation  methods  and  must  always 
be  protected  by  a  key,  and  the  manipulation  must  be  such  that 
the  key  is  closed  for  but  an  instant. 


MEASUREMENT  OF  POTENTIAL  DIFFERENCE    301 

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rents/' G.  L.  ADDENBROOKE,  The  Electrician,  vol.  45,  1900.  p.  901.  "The 
Electrostatic  Wattmeter,  Its  Calibration  and  Adaption  for  Polyphase 
Measurements,"  The  Electrician,  vol.  51,  1903,  p.  811.  "Ein  neues  Quad- 
rantenelektrometer  fur  dynamische  Messungen,"  H.  SCHULTZE,  Zeit.  fur 
Instrumentenkunde,  vol.  27,  1907,  p.  65.  For  a  more  complete  theory  of  the 
quadrant  electrometer  together  with  an  experimental  investigation  of  the 
instrument,  using  continuous  potentials  see  "  Elektrometrische  Unter- 
suchungen,"  E.  ORLICH,  Zeit.  fur  Instrumentenkunde,  vol.  23,  1903,  p.  97. 
For  a  discussion  of  the  instrument  as  used  in  power  measurements  at  the 
National  Physical  Laboratory  see  "The  Use  of  the  Electrostatic  System  for 
the  Measurement  of  Power,"  C.  C.  PATTERSON,  E.  H.  RAYNER,  C.  A. 
KINNES,  Journal  Institution  of  Electrical  Engineers,  vol.  51,  1913,  p.  294. 
A  valuable  bibliography  concerning  the  electrometer  is  included.  "Quad- 
rant Electrometers,"  W.  E.  AYRTON,  J.  PERRY  and  W.  E.  SUMPNER,  Phil. 
Trans.,  vol.  182,  1891,  p.  519. 

2.  "A   200,000-volt    Electrostatic   Voltmeter,"    A.  W.  COPLEY,  Electric 
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3.  Standardization    Rules,    American    Institute    of   Electrical   Engineers, 
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4.  "Dielectric  Phenomena  in,  High-voltage  Engineering,"   F.  W.  PEEK, 
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1913,  part  I,  p.  812. 

5.  "The  Dielectric  Strength  of  Air,"  ALEXANDER  RUSSELL,  Proc.  Physical 
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733. 

7.  "Calibration  of  the  Sphere  Gap  Voltmeter,"  L.  W.  CHUBB  and  C. 
FORTESCUE,  Trans.  American  Institute  of  Electrical  Engineers,  vol.  32,  1913, 
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8.  "Potentiometer  Installation,  Especially  for  High  Temperatures  and 
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9.  "A  New  Potentiometer,"  H.  B.  BROOKS,  Bulletin  Bureau  of  Standards, 
vol.  2,  1906,  p.  225.     "A  Deflection  Potentiometer  for  Voltmeter  Testing," 
H.  B.  BROOKS,  Bulletin  Bureau  of  Standards,  vol.  4,  1907-08,  p.  275.     De- 
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BROOKS,  Bulletin  Bureau  of  Standards,  vol.  8,  1912,  p.  395.     "Outline  of 
Design  of  Deflection  Potentiometers  with  Notes  on  the  Design  of  Moving 
Coil  Galvanometers,"  H.  B.  BROOKS,  Bulletin  Bureau  of  Standards,  vol.  8, 
1912,  p.  419. 


302  ELECTRICAL  MEASUREMENTS 

' 

10.  "  Thermokraftf reier  Kompensation  Apparatus,"   H.  DIESSELHORST, 
Zeit.  fur  Instrumentenkunde,  vol.  28,  1908,  p.  1. 

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DRYSDALE,  Phil.  Mag.,  vol.  17,  1909,  p.  402,  or  Proc.  Physical  Society  of 
London,  vol.  21,  1907-09,  p.  561. 

12.  LATIMER  CLARK,  Trans,  of  the  Royal  Society,  vol.  164,  1874,  p.  1. 

13.  "Clark  and  Weston  Standard  Cells,"  F.  A.  WOLFF  and  C.  E.  WATERS, 
Bulletin  Bureau  of  Standards,  vol.  4,  1907-08,  p.  1.     In  this  paper  will  be 
found  numerous  references  to  the  work  of  other  investigators. 

14.  "Announcement  of  the  Change  in  the  Value  of  the  International 
Volt,"  Proc.  American  Institute  Electrical  Engineers,  vol.  30,  p.  343.     Reprint 
of  Circular  No.  29  of  the  Bureau  of  Standards. 


CHAPTER  VI 
THE  MEASUREMENT  OF  POWER 

In  direct-current  circuits  the  measurement  of  power,  or  rate 
of  expenditure  of  electrical  energy,  is  best  accomplished  by  the 
use  of  calibrated  ammeters  and  voltmeters.  In  alternating- 
current  circuits  where  both  the  electromotive  force  (or  potential 
difference)  and  the  current  are  varying  from  instant  to  instant, 


FIG.  175. — Illustrating  instantaneous  and  average  power. 


passing  through  a  definite  cycle  of  values,  the  "  instantaneous 
power,"  or  the  power  being  given  to  the  circuit  at  a  particular 
instant  is  vi.  The  power  to  be  measured  is  the  average  value, 
of  vi  during  the  cycle, 

1  CT 
P  =  ~      vidt. 


303 


304  ELECTRICAL  MEASUREMENTS 

To  illustrate,  let  the  curves  of  voltage,  current,  and  vi  be  as 

shown  in  Fig.  175. 

pf 
The  net  area  under  the  power  curve  is  proportional  toL  vidt. 

T,  the  time  of  a  complete  cycle,  is  proportional  to  the  length  of 

1  CT 

the  base  line;  ~  I    vidt  is  therefore,  to   the  proper  scale,  the 
J  Jo 

average  ordinate  of  the  power  curve. 

In  general,  when  dealing  with  alternating-current  circuits  it 

1  CT 
is  necessary  to  have  methods  of  evaluating  —  I    vidt.     The  ex- 

IJQ 

pression  for  the  power  must  be  left  in  this  general  form,  for  in 
practical  measurements  it  is  not  permissible  to  make  any  as- 
sumptions as  to  the  forms  of  the  voltage  and  current  waves. 

For  general  purposes  the  simplest  and  most  satisfactory  method 
of  measuring  the  power  in  an  alternating-current  circuit  is  by  the 
use  of  the  electrodynamometer  wattmeter.  Other  methods  will 
be  discussed,  but  their  usefulness  is  restricted  to  particular  cases. 

The  Electrodynamometer  Wattmeter. — It  has  previously  been 
shown  that  any  electrodynamometer  measures  the  mean  product 
of  the  currents  flowing  in  the  fixed  and  movable  coils;  it  evaluates 


1  CT 
ij,  I    ifdi 


If  a  Siemens  dynamometer  is  connected  to  a  circuit  in  the 
manner  shown  in  Fig.  176,  the  fixed  coils  being  put  in  series  with 
the  load,  while  the  movable  coil,  in  series  with  a  suitable  non- 
reactive  resistance,  is  placed  across  the  line,  the  current  in  the 
fixed  coil,  IF,  is  the  instantaneous  load  current  and  the  current 
in  the  movable  coil,  iM,  is  proportional  to  the  instantaneous 
voltage. 

If  R  is  the  total  resistance  of  the  movable  coil  circuit,  iM  =  T>  ' 

In  the  case  of  the  Siemens  dynamometer  with  a  uniformly 
graduated  scale, 

KD  =  1 

K  is  a  constant  depending  on  the  windings  and  on  the  strength 
of  the  controlling  spring,  and  D  is  the  angle  through  which  it  is 


POWER  MEASUREMENT 


305 


necessary  to  twist  the  spring  in  order  to  bring  the  coil  back  to 
its  initial  position.  Substituting  the  above  values  for  the  cur- 
rents in  the  fixed  and  movable  coils, 


vidt 


or 


RKD  =  P 


(1) 


If  the  spring  is  perfect  and  the  scale  is  uniform,  the  power  is 
proportional  to  the  deflection. 


FIG.  176. — Showing  connections  of  wattmeter. 

The  only  assumption  involved  is  that  the  potential  circuit 
is  non-reactive.  The  influence  of  reactance  in  this  circuit  will 
be  discussed  later. 

The  relation  P  =  RKD  will  hold  for  any  wattmeter  where  the 
movable  coil  is  always  brought  back  to  a  definite  position  with 
respect  to  the  fixed  coil.  When  the  movable  coil  is  allowed  to 
ieflect  again'st  the  action  of  the  spring,  K  is  no  longer  a  constant, 
20 


306  ELECTRICAL  MEASUREMENTS 

for  it  depends  on  the  geometry  of  the  system  of  coils,  that  is, 
on  the  angle  between  the  coils,  and  this  angle  varies  with  every 
change  of  load.  In  consequence,  the  scales  of  portable  watt- 
meters are  generally  non-uniform.  Proper  proportioning  of  the 
relative  di'ameters  of  the  fixed  and  movable  coils  will  do  much 
toward  correcting  this,  see  page  80. 

Fig.  177  shows,  in  section,  one  form  of  portable  wattmeter 
which  is  in  common  use. 


Potential  Terminals       ^Current  Terminals 


di,-  u  uampifiq unamoer    \   .        .    -  ,, 

ohiela  fee  JsjJ?    7/          Movable  Coil 


FIG.  177. — Phantom  view  showing  construction  of  Weston  portable 

wattmeter. 

Heating  Losses  in  Wattmeters. — It  is  important  to  note  just 
what  a  wattmeter  measures.  P  in  formula  (1)  is  the  power 
given  to  the  circuit  by  the  current  which  flows  through  the 
fixed  coils,  that  power  being  expended  between  the  two  points 
at  which  the  potential  terminals  are  attached  to  the  circuit.  P 
therefore  must  include  the  heating  loss  either  in  the  current 
coils  or  in  the  potential  circuit,  depending  on  whether  the  point 
a  (Fig.  176)  is  on  the  supply  or  the  load  side  of  the  current  coils. 

Where  the  total  amount  of  power  is  small,  it  may  be  necessary 
to  correct  the  readings  for  the  loss  in  the  instrument  itself. 
The  two  possible  methods  of  connection  are  given  in  Fig.  178. 

With  connection  /  the  indication  of  the  wattmeter  includes 
the  PR  loss  in  the  current  coils;  with  connection  //  the  loss  in 


POWER  MEASUREMENT  307 

the   entire   potential    circuit   is   included.     The   corresponding 
corrections  when  a  small  output  is  measured  are  obvious. 

Compensation  for  Energy  Loss  in  the  Potential  Circuit.1— 
In  research  work  it  is  frequently  necessary  to  measure  small 
amounts  of  power,  a  few  watts,  and  in  this  case  the  loss  in  the 
potential  circuit, of  the  wattmeter  may  be  a  large  percentage  of 
the  power  to  be  determined.  To  avoid  the  necessity  of  making  a 
correction,  instruments  are  sometimes  so  designed  that  this  error 
is  compensated.  In  this  case  connection  II  is  used.  The  current 
which  flows  through  the  fixed  coil  is  made  up  of  two  components, 
one  due  to  the  load,  the  other  to  the  current  in  the  movable 
coil  circuit.  The  effect  of  this  last  must  be  compensated,  for 
the  magnetic  field  in  which  the  potential  coil  moves  is  due  to 
both  components.  If  a  second  winding,  coincident  at  all  points 


Load  <>R  §Load 


II 

FIG.   178. — Showing  wattmeter  connections. 

.with  the  regular  current  coil,  could  be  put  on  the  bobbin  carry- 
ing the  fixed  coil,  and  be  connected  into  the  potential  circuit  so 
that  its  effect  opposed  that  of  the  main-current  coil,  the  com- 
pensation would  be  exact;  for  instance,  if  the  load  circuit  were 
broken,  the  net  ampere-turns  acting  on  the  movable  coil  would 
be  zero  and  there  would  be  no  deflection.  As  the  two  coils 
cannot  be  made  coincident,  care  must  be  exercised  in  placing  the 
compensating  turns  so  that  when  the  load  circuit  is  broken,  the 
net  magnetic  field  at  the  movable  coil  will  be  zero  for  all  positions 
of  the  movable  coil.  Otherwise  the  degree  of  compensation 
will,  vary  with  the  scale  reading.  There  is  a  small  transformer 
action  due  to  the  mutual  inductance  of  the  two  windings  on  the 
fixed  c.oil,  but  in  commercial  measurements  at  the  usual  voltages 
.this  does  not  cause  an  appreciable  error. 

This  compensation  may  be  extended  so  that  the  power  lost 


308  ELECTRICAL  MEASUREMENTS 

in  a  voltmeter  connected  directly  across  the  load  may  be  allowed 
for,  a  second  compensating  winding  being  added  and  connected  in 
series  with  the  voltmeter;  allowance  must  be  made  for  the 
'  changed  resistance  of  the  voltmeter  circuit. 

Grouping  of  Instruments. — The  heating  losses  have  a  bearing 
on  the  grouping  of  the  instruments  when  the  voltage,  current, 
power  and  power  factor  of  a  small  reactive  load  are  to  be 
determined. 

Electrical  apparatus  is  generally  sold  to  be  operated  at  some 
definite  voltage,  so  the  voltmeter  is  placed  across  the  load  as 
in  Fig.  179. 

As  shown,  the  wattmeter  measures  in  addition  to  the  load, 
the  power  in  its  own  current  coils,  in  the  ammeter,  and  in  the 

voltmeter.     The   ammeter   gives 
the  vector  sum  of  the  currents  in 
the  load  and  in  the  voltmeter. 
Load       Errors  due  to  Local  Fields.— In 
industrial  testing,  it  is  not  safe 
to  assume  that  a  wattmeter  will 
be    uninfluenced    by    local    mag- 
FIG.  179  —Showing  grouping  of  netic  fieldg>      In  the  ordinary  port- 
instruments  for  measuring,  power,  . 
current  and  voltage.                         able    instruments    this    error,    if 

present,  will  depend  on  the  de- 
flection. Its  presence  or  absence  may  be  made  obvious  by 
connecting  the  potential  coil  alone  to  the  circuit  and  observ- 
ing the  deflection  when  the  instrument  is  turned  to  several 
different  azimuths.  If  the  error  is  present  and  it  is  not  feasible 
to  change  the  location  of  the  observing  station,  the  instrument 
may  be  turned  to  the  position  where  the  pointer  is  undeflected, 
that  is,  where  the  movable  coil  is  threaded  by  the  maximum 
number  of  lines  of  force,  due  to  the  stray  field.  When  the 
proper  position  has  been  found,  the  direction  of  the  pointer 
may  be  noted.  If  in  the  subsequent  use  of  the  wattmeter  the 
pointer  is  always  kept  in  approximately  this  direction,  the  body 
of  the  instrument  being  turned  as  the  load  is  varied,  the  error 
will  be  rendered  negligible,  provided  the  direction  of  the  local 
field  does  not  change. 

Direct-current  stray  fields  have  no  influence  on  the  readings 
when  alternating  currents  are  being  dealt  with,  and  alternating 


POWER  MEASUREMENT  309 

stray  fields,  to  have  any  effect,  must  be  of  the  frequency  of  the 
current  under  measurement. 

As  high-capacity  instruments  have  comparatively  few  turns 
on  the  fixed  coil,  special  care  must  be  taken  that  there  are  no 
loops  in  the  leads  near  the  instrument  and  that  the  current 
leads  occupy  the  same  position  with  respect  to  the  instrument 
during  its  calibration  and  subsequent  use. 

To  obviate  stray  field  errors,  the  working  parts  of  the  instru- 
ment are  frequently  surrounded  by  a  soft  iron  shield  built  up 
of  stampings  (see  Fig.  177). 

Voltage  between  Current  and  Potential  Coils. — The  movable 
coil  of  a  wattmeter,  being  in  series  with  a  large  resistance,  may 
inadvertantly  be  connected  to  the  circuit  so  that  practically 
the  full  line  potential  exists  between  the  current  and  the  potential 
coils.  This  may  give  rise  to  errors  due  to  the  electrostatic 
attraction  between  these  two  coils;  also  there  is  danger  that  the 
insulation  between  the  coils  may  be  punctured.  The  connec- 
tions should  be  so  made  that  the  current  and  potential  coils 
are,  as  nearly  as  possible,  at  the  same  potential.  If  when  so 
connected,  the  deflection  is  in  the  wrong  direction,  the  current 
coil  should  be  reversed.  The  proper  position  of  a  multiplier, 
when  one  is  used,  is  governed  by  the  same  consideration. 

It  is  well  to  mark  the  terminals  of  a  wattmeter  once  for  all 
so  that  there  can  be  no  mistake  in  making  the  connections. 
Such  a  marking  also  obviates  any  question  as  to  the  algebraic 
sign  of  the  readings  when  measuring  polyphase  power. 

When  instrument  transformers  are  used,  electrostatic  troubles 
may  be  avoided  if  the  two  coils  of  the  wattmeter  be  connected 
by  a  piece  of  very  fine  fuse  wire. 

The  Effect  of  Reactance  in  the  Potential  Circuit. — It  has  been 
assumed  that  the  potential  circuit  is  non-reactive;  this  can 
never  be  strictly  true  since  it  must  contain  the  movable  coil. 
In  commercial  instruments,  when  used  at  ordinary  frequencies 
and  power  factors,  the  resistance  of  the  potential  circuit  is  so 
high  in  comparison  with  its  reactance  that  the  effect  of  the 
inductance  is  entirely  negligible.  In  special  investigations,  how- 
ever, cases  arise  where  the  utmost  care  must  be  exercised  if 
reliable  results  are  to  be  obtained.  The  presence  of  reactance 
has  two  effects:  it  cuts  down  to  a  certain  extent  the  current 


310  ELECTRICAL  MEASUREMENTS 

in  the  potential  coil  and  shifts  its  phase  by  an  amount  dependent 
on  the  frequency.  Thus  the  mean  product  of  the  currents  in 
the  fixed  and  movable  coils  is  altered  from  its  proper  value. 
If  sinusoidal  currents  are  assumed,  the  magnitude  of  the  error 
thus  introduced  may  readily  be  computed. 

Symbols  used  in  the  Discussion  of  the  Theory  of  the  Wattmeter 
Maximum  values  of  currents  and  voltages  are  denoted  by  large  letters, 
instantaneous  values  by  small  letters. 

Referring  to  Fig.  180 

ab  =  V  =  voltage  at  terminals  of  potential-coil  circuit. 
IP  =  current  in  potential  coil. 
RP  =  resistance  of  potential-coil  circuit. 

ac  =  IpRp  =  ohmic  drop  in  potential-coil  circuit. 

IL  —  current  in  load. 

RL  =  resistance  of  load. 

EC  =  resistance  of  current  coils. 

Jc    =  current  in  current  coils. 

ad  ==  IL(RL  +  RC)  ohmic  drop  in  load  circuit  between  potential  terminals. 

dp  =  phase  displacement  in  potential-coil  circuit. 

QL  —  phase  displacement  in  load  circuit  between  potential  terminals. 
LP  =  inductance  of  potential-coil  circuit. 
LL  =  indutance  of  load. 
Lc  —  inductance  of  current  coils. 
ZL,  =  impedance  of  load. 
Zp  —  impedance  of  potential-coil  circuit. 
Zc  =  impedance  of  current  coils. 

co  =  2  TT  times  frequencjr. 

m  =  mutual  inductance  of  fixed  and  movable-coil  circuits. 
PL  —  power  in  load. 

pw  =  power  as  read  from  the  wattmeter. 
HP  =  heating  loss  in  potential  circuit. 
He  =  heating  loss  in  current  coils. 

K  =  constant  of  dynamometer. 
'    D  =  deflection  of  instrument. 

Consider  case  7  on  page  307  where  the  current  coils  are 
traversed  by  the  load  current  only  and  the  power  measured 
includes  the  heating  loss  in  the  current  coils. 

On  account  of  the  power  factor  of  the  reactive  load  circuit,  the 
current,  IL,  will  lag  behind  V  by  an  angle  6L,  und  in  consequence 
of  the  reactance  of  the  potential-coil  circuit,  the  current  in  it  will 
be  out  of  phase  with  V  by  an  angle  BP  and  will  be  altered  from 

the  value  -5-  to  — 5 — -,  see  Fig.  180. 
rip  ftp 


POWER  MEASUREMENT 


311 


The  deflection  of  the  instrument  is  proportional  to  the  mean 
product  of  the  instantaneous  values  of  IP  and  7L,  therefore, 


iLiPdt  =  l-Llp  cos  (BL  -  BP}. 


KD  =   1T   ['i. 

i  Jo 

So  the  apparent  power  or  the  scale  reading  is 


=  IL 


i>  cos  (BL  -  Br)   =PW 


(2) 


The  true  power,  that  is  the  power  which  would  be  read  from 
the  scale  if  there  were  no  reactance  in  the  potential  circuit, 
is  given  by 

PL+H,.  =  /L0T'co,s  BL  (3) 


FIG.  .ISO.1 — Pertaining  to  effect  of  inductance  in  the  potential  circuit  of  a 

wattmeter. 

A  correction  to  be  subtracted  from  the  apparent  power  in 
order  to  obtain  the  true  power  may  be  determined,  for  by  (2) 

ILV  cos  6P  ILV 

Pw  =  ~    — 2~    -  cos  (6L  -  Or)  =     2 

(cos2  OP  cos  BL  +  cos  BP  sin  dp  sin  BL) 

.'.  PL  +  Hc  =    ~-     70  V    ^an   OP  sm  OL. 

In  portable  instrument's  the  angle  dP  is  a  very  small  fraction  of  a 
degree  but  in  commutating  watt-hour  meters,  such  as  were 
formerly  used  on  alternating-current  circuits,  it  may  be  as  large 
as  2°.  Using  the  values  of  the  current  and  voltage  given  by 


312  ELECTRICAL  MEASUREMENTS 

indicating  instruments,  instead  of  maximum  values,  and  remem- 
bering that  ordinarily  BP  is  very  small, 

PL  +  Hc  =  Pw  -  ILV  tan  BP  sin  BL  =  Pw  -  ILV  (~^-\  sin  0L  (4) 


The  effect  of  the  phase  displacement  in  the  potential  circuit 
evidently  depends  on  the  frequency  and  on  the  characteristics 
of  the  load  as  well  as  on  the  wattmeter  itself.  It  increases 
as  the  power  factor  of  the  load  is  decreased  and  at  extremely 
low  power  factors  extraordinary  precautions  must  be  taken  in 
order  to  procure  accurate  results. 

If  the  resistance  of  the  potential  circuit  is  exceedingly  high, 
there  may  be  capacity  effects  in  the  series  resistance.  Some  in- 
struments are  so  designed  that  a  part  of  the  potential  circuit  is 
coiled  on  a  metal  bobbin  and  although  this  is  split  lengthwise  it 
is  not  entirely  free  from  eddy  currents.  Both  the  capacity  and 
the  eddy  currents  modify  the  phase  displacement. 

If  the  load  current  is  leading  and  the  power  factor  very  low, 
the  wattmeter  readings  tend  toward  zero  and  at  some  particular 
value  of  the  power  factor  the  reading  will  reverse.  For  an 
interesting  case  in  point,  see  Journal  of  the  Institution  of  Electrical 
Engineers,  vol.  30,  1901,  p.  467. 

The  ratio  of  the  true  to  the  apparent  power  is 

PjA-JIc  =   F  _COS_fc 

Pw  cos  BP  cos  (0L  -  BP) 

and  the  total  power  is  obtained  by  multiplying  the  apparent 
power  by  the  correction  factor  F. 

The  trigonometrical  form  of  this  expression  may  be  changed 
so  that  the  tangents  rather  than  the  cosines  of  the  angles  may 
be  used,  then 

1  +  tan*  BP 
1  +  tan  Op  tan  BL 

This  is  the  usual  form  of  the  correction  factor. 

If  there  are  no  modifying  causes  such  as  capacity  or  eddy- 
current  effects,  tan  BP  may  be  expressed  in  terms  of  the  inductance 
and  resistance  of  the  potential  circuit.  Then 


1   + 

F  =  — XJtp/ (7) 

/Lpco\    /, 
1  +    1-b-        tan 


POWER  MEASUREMENT  313 

It  is  preferable  to  use  the  correction  term  of  equation  (4)  rather 
than  the  factor  given  in  equation  (7),  for  the  latter  becomes 
practically  indeterminate  at  low  power  factors. 

Compensation  for  the  Inductance  of  the  Potential  Circuit.3— 
It  naturally  suggests  itself  that  the  effect  of  inductance  in  the 
potential  circuit  may  be  annulled  by  the  use  of  capacity.  Simple 
tuning  of  the  circuit  is  manifestly  inadequate,  for  the  arrange- 
ment must  be  such  as  to  be  practically  independent  of  the 
frequency,  in  order  that  there  may  be  no  errors  when  dealing 
with  non-sinusoidal  waves. 

The  arrangement  used  for  this  purpose  by  Abraham  and  Rosa 
is  a  condenser  inserted  in  series  with  the  movable  coil  and 
shunted  by  a  non-inductive  resistance.  Such  an  arrangement 
may  be  adjusted  so  that,  for  all  practical  purposes,  the  net 
reactance  of  the  circuit  is  reduced  to  zero. 

The  connections  of  the  potential  circuit  then  become  those 
shown  in  Fig.  181. 


c 

FIG.  181.  —  Showing  method  of  compensating  the  inductance  of  the  potential 
circuit  of  a  wattmeter. 

The  impedance  between  a  and  b  is 

1  r  r  - 

ab  ~ 


1  ~  1  +  jcoCr       1  +  co2C2r2 

r 


The  impedance  between  b  and  c  is 
Zbc  =  R  +  j 
Therefore  the  total  impedance  is 

M  _   /i,  ./^^2  / 

Zac  ==  R  +  jcoL  +  -ji---^  =  ( 


R 


314  ELECTRICAL  MEASUREMENTS 

If  co2C2r2  can  be  neglected  in  comparison  with  unity 

Zac  =  R  +  r  +  j«(L  -  Cr2)  approx.  (8) 

If  r  is  adjusted  so  that 

L  =  Cr2 
then 

Zar  =  R  +  r 

which  is  the  resistance  of  the  circuit  as  measured  by  a  bridge. 
As  long  as  the  term  co2C2r2  is  negligible,  the  compensation  will 
not  be  affected  by  the  frequency. 
As  an  example,  consider  the  following  data: 

L  =  0.000328  henry 

R  =  20  ohms 

C  =  1  microfarad 

r    =  \  f±f  as  18.11  ohms. 


Using  these  values  the  impedances  and  .phase  displacements  at 
60  and  1,000  cycles  per  second  are: 


Z60     =  38.109  +jQ.  000016 
060      =  0°.  000024 

Zi.ooo  =  37.878  +  JO.  0265 
0li000    =  0°.040 

If  no  compensation  is  applied  the  values  are 

Z6Q     =38.11  +  J0.124 
0G,      =0°.186 
Zi.ooo  =38.11  +J2.06 
0i,ooo    =  3°.l 

To  determine  whether  compensation  is  needed  and  to  make  the 
necessary  adjustments,  the  potential  circuit  is  short-circuited 
on  itself  and  a  large  alternating  current  sent  through  the  fixed 
coil. 

The  instrument  will  remain  undeflected: 

1.  If  there  be  no  mutual  induction  between  the  two  coils. 

2.  If  the  effective  inductance  of  the  movable-coil  circuit  is 
zero,  for  then  the  currents  in  the  movable  and  fixed  coils  will  be 
in  quadrature. 

Having  made  sure  that  the  mutual  induction  is  not  zero,  the 
resistance  r  may  be  adjusted  until  the  deflection  disappears. 


POWER  MEASUREMENT 


315 


The  adjustment  is  then  complete,  provided  there  are  no  eddy- 
current  effects  in  the  fixed  coil  or  in  the  frame  of  the  instrument 
(see  page  316).  These  effects  are  discussed  in  the  original 
paper  by  Rosa. 

Effect  of  Mutual  Induction  between  Fixed  and  Movable  - 
coil  Circuits. — In  the  previous  discussion  no  reference  has  been 
made  to  the  possible  effects  of  mutual  induction  between  the 
current  and  potential  circuits.  In  commercial  instruments 
these  effects  are  so  small  as  to  be  negligible.  They  might,  how- 
ever, be  worthy  of  consideration  in  special  low-voltage  wattmeters 
where  an  attempt  is  made  to  attain  a  maximum  of  sensitivity. 

When  the  instrument  is  read  by  a  torsion  head  the  mutual 
inductance  can  be  made  zero,  but  if  the  movable  coil  is  •allowed 


I  II 

FIG.  182. — Pertaining  to  effect  of  mutual  induction  in  wattmeter. 

to  deflect,  the  mutual  inductance  will  have  an  effect  dependent 
on  the  reading  of  the  instrument,  being  zero  and  changing  sign 
when  the  planes  of  the  coils  are  perpendicular. 

Take  the  connections  shown  in  Fig.  1827  which  are  the  same 
as  those  assumed  in  Fig.  180. 

Equating  the  values  of  the  P.D.  between  1  and  7  reckoned 
via  the  load  and  via  the  potential  circuit  gives 


IZS(ZL  ~h  Zc)   +  JWW/68  — 

r(flL  +  Bc)  +  jw 

^f)6    =    If-1  - 


=    /2*[ 


RP(Ri 


Rc) 


+  jraw/23 

») 


'2(/>L  +  Lc  ±  ra)  (LP  ±  ra) 

The  current  in  the  potential  coil  is  seen  to  consist  of  two 
components,  one  in  phase  and  one  in  quadrature  with  the  current 
in  the  fixed  coils,  /2s,  which  is  also  the  load  current  //,. 


316  ELECTRICAL  MEASUREMENTS 

The  turning  moment,  and  therefore  the  deflection,  are  pro- 
portional to  the  mean  product  of  the  currents  1 23  and  756  and 
this  mean  product  multiplied  by  the  resistance  of  the  potential 
circuit  is  the  reading  of  the  wattmeter.  Using  effective  values, 
power  by  wattmeter  = 

7?  rr>       T  ,rft2(ft  +  R^  +  ^Rp(LL  +  Lc±m)  (LP  ±  m)-] 

ft2  +  co2(Lp  ±  m)2 

The  instrument  should  give  the  power  in  the  load  circuit 
between  the  points  1  and  4,  that  is  the  power  in  the  load,  plus 
the  heating  in  the  current  coils. 

PL  +  HC  =  IS(RL  +  Rc) 


-]- 


Eddy-current  Errors. — Another  source  of  error,  one  not 
amenable  to  calculation,  may  be  found  in  instruments  of  faulty 
design.  It  is  that  due  to  currents  induced  in  masses  of  metal, 
such  as  the  frame  of  the  instrument,  or,  in  instruments  of  large 
current  capacity,  in  the  current  coils  themselves,  for  these 
coils  must  be  made  very  massive  in  order  to  give  the  requisite 
carrying  capacity. 

This  error  should  be  reduced  to  a  minimum  by  the  design  of 
the  instrument.  In  high-capacity  instruments  it  will  be  nec- 
essary to  wind  the  current  coil  with  a  stranded  conductor  or  its 
equivalent,  the  strands  being  insulated  from  one  another. 
Great  care  must  be  taken  in  arranging  them.  The  average 
position  of  each  strand  in  the  cross-section  should  be  the  same 
as  that  of  every  other  strand,  otherwise  the  heating  of  the  coil 
may  change  the  current  distribution  and  therefore  the  calibra- 
tion of  the  instrument. 

In  laboratory  instruments  intended  for  heavy  currents,  the 
current  coil  may  be  made  of  a  small  and  thin  copper  tube  through 
which  there  is  a  rapid  circulation  of  water. 

To  detect  the  presence  of  eddy-current  errors  in  research  in- 
struments where  the  inductance  of  the  potential-coil  circuit  is 
compensated,  the  zero  reading  is  brought  to  a  noted  point  on 
the  scale  and  the  compensation  for  the  inductance  of  the  moving- 
coil  circuit  made  as  shown  on  page  313.  The  zero  is  then  changed 


POWER  MEASUREMENT  317 

by  use  of  the  torsion  head  and  the  compensation  tested  at  various 
points  along  the  scale.  If  the  eddy-current  error  is  absent,  the 
adjustment  of  the  potential  circuit  for  zero  effective  inductance 
will  be  the  same  at  all  points. 

OTHER  METHODS  OF  MEASURING  POWER 

In  consequence  of  the  development  of  the  wattmeter,  the 
three  methods  now  to  be  described  are  merely  of  historical 
interest  as  methods  for  power  measurement.  However,  two 
of  them  have  other  applications  which  are  still  of  practical  value. 

The  Three  Dynamometer  Method. — The  connections  are  as 
shown  in  Fig.  183.  At  DI,  D2  and  D3  are  three  electrodyna- 


Load 


Dl 

FIG.  183.  —  Connections  for  three  dynamometer  method  for  power 
measurement. 

mpmeters  each  with  its  fixed  and  movable  coils  in  series.  R 
is  the  total  resistance  of  the  circuit  of  D2.  The  instan- 
taneous values  of  the  currents  are  as  indicated.  In  general 


R  is  assumed  to  be  non-inductive  so, 

i  r 

P  =  R  ^ 

IJo 
At  any  instant 

ii  =  it  +  iz 
and 


so 


318  ELECTRICAL  MEASUREMENTS 

and 


The  three  integrals  are  the  mean  square  values  of  the  three 
currents  and  will  be  given  by  the  readings  of  the  dynamometers. 
If  Siemens  instruments  are  used, 

(*T 
i^dt 

where  KI  is  the  constant  of  the  instrument  and  DI  its  deflection, 

and  similarly  for  the  other  instruments. 

Hence 

~P     _    ("  T£     T\          _     T£     T\          _     7^"     T\    1  /  -I  O  \ 

The  result  involves  no  assumption  as  to  wave  form.  It  does 
assume  that  the  resistance,  R,  is  non-inductive.  This  cannot 
be  exactly  true  for  the  potential  circuit  contains  the  electro- 
dynamometer.  The  use  of  hot-wire  ammeters  would  render  this 
assumption  practically  true.  P  includes  the  power  in  D^. 

The  results  are  greatly  affected  by  the  errors  of  reading.  To 
obtain  the  best  precision  in  the  measurement,  the  power  wasted 
in  R  must  be  equal  to  the  load,  an  obviously  impracticable 
condition. 

This  method  is  used  in  telephone  investigations  as  an  aid  to 
determining  line  constants. 

The  Three  Voltmeter  Method. — In  this  analogous  method  the 
three  instruments  capable'  of  measuring  the  mean  square  values 
of  the  currents  are  replaced  by  three  instruments  which  measure 
mean  square  voltages.  The  connections  are  as  shown  in  Fig.  184. 

The  non-inductive  resistance  R  is  joined  in  series  with  the 
load  and  the  three  voltages  read,  as  indicated. 

P  =  i  riv,dt  =  Li(T 

At  any  instant 


POWER  MEASUREMENT 


319 


If  the  voltmeters  are  of  the  electrodynamometer  or  the  electro- 
static type, 


P  = 


(15) 


Load 


FIG.  1 84.— Connections  for  three-voltmeter  method  for  power  measurement 

For  the  greatest  precision  the  power  wasted  in  R  must  be  equal 
to  the  load.     P  includes  the  power  in  F3. 

The  Split-dynamometer  Method. — The  connections  are  shown 
in  Fig.  185. 


Load. 


FIG.   185. — Connections  for  split-dynarnorneter  method  for  power 
measurement. 

Ds  is  an  ordinary  current  electrodynamometer  with  its  coils 
in  series.  FM  is  another  dynamometer  with  a  non-inductive 
resistance,  R,  tapped  in  between  the  fixed  and  movable  coils. 


At  any  instant 


i  r         i  cr 

=  rr\    vi3dt  =  R-  „!    i 
IJo  J-  Jo 


1 1  r  1  rlf      i 

P  =  R\rrl    iiitdtt-  Tl    i**dt\.  (16) 

L  -/  JO  1  JO 


320 


ELECTRICAL  MEASUREMENTS 


The  split  dynamometer  gives  the  mean  product  of  the  currents 
in  its  coils,  so 

P  =  R(K1D1  -  KaDB].  (17) 

Potier  Method  for  Power  Measurement — The  Electrostatic 
Wattmeter.4 — The  electrostatic  wattmeter  is  an  instrument  of 
importance  in  research  work,  its  particular  field  of  usefulness 
being  the  measurement  of  small  amounts  of  power  at  high  vol- 
tage and  low  power  factor.  It  is  also  used  at  the  National 
Physical  Laboratory,  London,  in  the  testing  of  watt-hour  meters. 

This  method  for  the  measurement  of  electrical  power  was 
first  given  by  A.  Potier.  The  readings  are  obtained  by  using  a 
quadrant  electrometer.  In  the  original  arrangement,  a  non- 
reactive  resistance  is  joined  in  series  with  the  load  and  the  two 


Load 


FIG.  186.—  Connections  for  Potier  method  for  power  measurement. 

pairs  of  quadrants  connected  to  its  terminals.  Two  readings 
are  then  taken,  one,  with  the  needle  connected  to  the  load  ter- 
minal on  the  far  side  of  the  line,  and  another,  with  the  needle 
connected  to  the  other  load  terminal.  The  connections  are  shown 
in  Fig.  186.  It  has  previously  been  shown  that  with  the  instan- 
taneous potential  differences  indicated  at  A,  the  deflection  of  the 
quadrant  electrometer  may  be  expressed  by 


D  =  K~ 


When  the  connection  is  at  a,  if  the  charging  current  for  the 
electrometer  be  neglected, 


Da  =  K 


d*dt 


].(lS) 


POWER  MEASUREMENT  321 

i  r 

The  term  =  I    d2dt  is   evaluated  by  the  second  reading,   for 
1  Jo 

with  the  connection  at  6  the  deflection  is 


Db  is  dependent  on  the  power  wasted  in  the  non-reactive  resist- 
ance. 

The  necessity  for  taking  the  second  reading  may  be  obviated 
by  a  method  given  by  Miles  Walker4. 

The  connections  are  shown  in  Fig.  187. 

r,L=0 


& 


jLoad 


c  _ 

FIG.  187. — Connections  for  electrostatic  wattmeter. 

Two  non-inductive  resistances,  R  and  r,  are  placed  in  series 
with  the  load  and  in  the  positions  indicated;  the  needle  is  con- 
nected to  some  form  of  potential  divider  so  that  its  potential 
with  reference  to  the  quadrants  is  only  a  fraction  of  the  line  vol- 
tage. The  potential  divider  may  be  a  high  resistance,  but  it  is 
better  to  provide  taps  on  the  secondary  of  the  high  voltage 
transformer,  for  in  this  case  the  potential  of  the  point  b  is  not 
disturbed  by  the  charging  current  flowing  to  the  needle. 
Let 

Vac    _ 
Vbc   ~ 

then 


"•»  =  »«  (-1  -  n) 


The  voltage  between  quadrant  (2)  and  the  needle  is  (see  Fig.  187), 
21 


322  ELECTRICAL  MEASUREMENTS 

if    the   charging   current    for   the   electrometer    be    neglected, 
«*  =  v  +  ri  -(Ri  +  v  + 

Consequently 


The  term  -  -  is  proportional  to  the  instantaneous  power;  the 

ft/ 

other  three  terms  can   be  eliminated  by  properly   adjusting  r, 
for  if  their  sum  be  placed  equal  to  zero, 


n 

.  (2D 

If  r  be  adjusted  to  this  value, 


2KR  i  r 

D  =  -    -  ™  I    weft 

w     -/Jo 


or 

(22) 


and  no  correction  for  the  power  wasted  in  R  is  necessary. 

If  the  tap  be  brought  out  at  the  middle  of  ac,  n  =  2,  and  no 
compensating  resistance,  r,  is  required. 

If  the  compensating  resistance  is  not  used,  (r  =  0), 


nD 


-2KR  +  I2R(-2-) 

When  small  amounts  of  power  at  low  power  factor  are  measured, 
the  term 


POWER  MEASUREMENT 


323 


which  gives  the  correction  for  the  power  in  the  resistance  R, 
may  become  very  important.  If  n  is  2  the  instrument  gives  the 
power  without  correction. 

When  the  electrostatic  wattmeter  is  used  in  connection  with  a 
fictitious  load  (see  page  500)  in  the  calibration  of  power  and 
energy  meters,  the  correction  term  due  to  the  power  loss  in  the 
series  resistance  will  be  eliminated  if  the  current  and  voltage 
circuits  are  electrically  connected  at  the  middle  of  the  resistance, 
R,  as  shown  in  Fig.  188. 


To  Source  of 
Voltage 


Wattmeter 
(Under  Test 


Source  of  Current 

Phase  Variable 
FIG.  188. — Connections  for  electrostatic   wattmeter   with   fictitious   load. 

In  this  case,  the  potential  difference  between  quadrant  2  and 
the  needle  is 

d       v 


"P.2"  (24, 

This  method  of  connection  is  used  in  a  highly  developed 
form  at  the  National  Physical  Laboratory,  for  calibrating  com- 
mercial instruments. 

The  electrostatjc  wattmeter  has  been  used  in  measurements  of 
the  power  lost  in  dielectrics  at  high  voltages,  as  in  cables  run- 
ning without  load,  in  condensers  and  in  samples  of  insulating 
material. 

In  testing  small  samples  of  insulating  materials  at  high  vol- 
tages, it  is  necessary  to  avoid  measuring  the  energy  dissipated 
in  the  air  around  the  electrode  and  on  the  surface  of  the  sample. 


324 


ELECTRICAL  MEASUREMENTS 


For  this  reason  Rayner  used  a  guard-ring  electrode  as  shown 
in  Fig.  190. 


FIG.  189. — Quadrant   electrometer  used   at  National  Physical  Laboratory 
as  an  electrostatic  wattmeter. 


The  current  for  the  guard  ring  is  furnished  directly  from 
the  transformer  and  is  not  included  in  the  measurement. 


POWER  MEASUREMENT 


325 


Sources  of  Error.4 — When  measuring  small  amounts  of 
power  the  resistance  R  must  be  large.  This  produces  two  re- 
sults; the  condensers  formed  by  quadrant  2  and  one-half  of  the 
needle  must  be  charged  through  this  resistance,  while  that  formed 
by  the  quadrant  1  and  the  other  half  of  the  needle  is  charged 
directly  from  the  source.  Consequently  the  potential  of  the 
condenser  formed  by  the  needle  and  quadrant  2  is  a  trifle  lower 
than  it  should  be,  the  time-phase  relation  of  the  potentials  on  the 
two  condensers  is  not  quite  correct  and  the  result  is  that  with 
the  main  circuit  open  there  will  be  a  small  deflection.  A  high 
resistance  also  alters  the  power  factor  of  the  circuit  which  in 
testing  insulating  materials  may  be  very  low.  The  current  must 
be  relatively  high,  and  the  correction  term  in  (23)  becomes  large. 


FIG.   190. — Illustrating  Rayner  guard-ring  electrode. 

The  net  error  is  practically  proportional  to  R.  When  in- 
vestigating dielectric  losses  a  correction  can  be  made  with 
sufficient  accuracy  by  observing  the  deflection  with  two  known 
values  of  R  and  extrapolating  for  the  watts  expended  when 
R  =  0. 

If  the  needle  is  not  tapped  into  the  transformer  but  is  en- 
ergized from  a  potential  divider,  an  error  may  be  introduced  be- 
cause of  the  alteration  of  the  potential  of  the  point  6,  Fig.  187, 
due  to  the  charging  current  necessary  for  the  needle.  Errors 
may  also  arise  from  capacity  effects  in  very  high  resistances  of 
the  ordinary  construction.  In  electrostatic  wattmeters  for  use 
at  high  voltage  it  is  essential  that  there  be  ample  separation  be- 
tween the  quadrants  and  the  needle  so  that  brush  discharges 
will  be  avoided. 


326 


ELECTRICAL  MEASUREMENTS 


Ryan  Power  Diagram  Indicator.5 — The  Ryan  Power  Dia- 
gram Indicator  is  a  device  in  which  the  electrostatic  tube  (see 
page  647)  is  employed  to  trace  diagrams,  the  areas  of  which  are 
proportional  to  the  power  supplied  to  the  load.  Its  particular 
field  of  usefulness  is  the  measurement  of  small  amounts  of  power 
at  high  voltage.  It  has  been  applied  to  the  measurement  of 
corona  losses  and  to  the  total  losses  in  samples  of  insulating 
materials.  Losses  as  small  as  0.03  watt  at  9,000  volts  have  been 
measured.  The  accuracy  of  the  original  arrangement  was  about 
5  per  cent.  The  application  of  the  device  (sometimes  called 
the  cyclograph)  to  the  investigation  of  the  behavior  of  insulating 
materials  has  been  developed  by  Minton.6 


Primary  of 
Supply  Transformer 

FIG.  191. — Connections  for  Ryan  power  diagram  indicator. 

In  order  to  obtain  the  diagram,  it  is  necessary  to  employ  two 
sets  of  electrodes.  One  set  is  arranged  to  deflect  the  fluorescent 
spot  along  the  X-axis  on  the  screen;  another,  along  the  F-axis. 

Looking  along  the  axis  of  the  tube,  the  electrodes  are  placed 
as  shown  in  Fig.  191,  which  also  shows  the  other  connections. 

To  employ  this  arrangement,  one  must  be  able  to  divide  the 
secondary  of  the  testing  transformer  into  two  equal  sections  so 
that  the  two  condensers  CC  may  be  inserted  between  them. 
The  junction  of  the  condensers  is  grounded.  By  means  of  the 
electrodes,  TI,  the  fluorescent  spot  is  at  every  instant  deflected 
along  one  coordinate  on  the  screen  proportionally  to  v.  The 
electrodes,  T2,  cause  the  spot  to  be  deflected  along  the  other 
coordinate  proportionally  to  the  instantaneous  values  of  Vi, 


POWER  MEASUREMENT 


327 


the  potential  difference  between  the  outer  terminals  of  the  con- 
densers C. 

Let  the  displacement  along  y  be 


y  =  Kv 


and  that  along  x  be 


K  and  Kf  are  constants. 

Then  for  an  elementary  area,  dA  =  ydx  =  KK'vdvi. 


FIG.  192. — Connections  for  Ryan  power  diagram  indicator  with  condenser 

multiplier. 

The  current  i  through  the  condensers  is  that   taken  by  the 
specimen,  and 

C  dvi 


Then 


2   dt 


..       2KK'    ..4 
dA  =  — -^ —  vidt 


and  the  area  of  the  diagram  is 

A  =  K"  \    vidt  =  k'P. 
Jo 

The  constant  k'  is  determined  by  calibration. 


(25) 


328  ELECTRICAL  MEASUREMENTS 

Any  losses  in  the  insulation  or  oil  used  in  the  transformer 
are  included  in  the  measurement,  so  the  oil  should  be  specially 
dried.  The  condensers  CC  may  be  oil-immersed.  Perfectly 
dry  oil  must  be  used  so  that  the  dielectric  may  be  as  free  from 
losses  as  possible. 

With  the  arrangement  as  just  described  the  potential  difference 
to  give  a  full-scale  deflection  is  only  a  few  hundred  volts.  To 
adapt  the  arrangement  to  high-voltage  work,  the  voltage  v 
must  be  applied  to  the  electrodes,  TI,  by  means  of  a  con- 
denser multiplier,  as  shown  in  Fig.  192. 

The  voltage  vi  which  is  dependent  on  the  current  is  obtained 
as  before.  The  plates  of  the  condenser  multiplier  are  at  a,  b,  c, 
d,  and  by  adjusting  the  position  of  the  plates  a  and  d,  the  multi- 
plying power  may  be  varied  as  desired.  Air  condensers  are  used. 
In  the  original  apparatus  the  " plates"  a  and  d  were  long  sheet- 
metal  cylinders  with  hemispherical  ends.  They  were  hung  by 
insulating  cords  so  that  they  could  be  readily  raised  or  lowered. 
By  this  means  the  range  of  the  instrument  could  be  increased 
to  250,000  volts. 

POWER  MEASUREMENT  IN  POLYPHASE  CIRCUITS 

Blondel's  Theorem.7 — If  energy  be  supplied  to  any  system 
of  conductors  through  n  wires,  the  total  power  in  the  system  is 
given  by  the  algebraic  sum  of  the  readings  of  n  wattmeters,  so 
arranged  that  each  of  the  n  wires  contains  one  current  coil,  the 
corresponding  potential  coil  being  connected  between  that  wire 
and  some  point  on  the  system  which  is  common  to  all  the  poten- 
tial circuits.  If  this  common  point  is  on  one  of  the  n  wires  and 
coincides  with  the  point  of  attachment  of  the  potential  lead  to 
that  wire,  the  measurement  may  be  effected  by  the  use  of  n  —  1 
wattmeters. 

The  receiving  and  generating  circuits  may  be  arranged  in  any 
desired  manner  and  no  assumption  is  made  as  to  the  way  in  which 
the  e.m.fs.  and  currents  vary. 

To  prove  the  theorem,  denote  by  the  subscripts  1,  2,  3,   .    .    . 
n   the  different  supply    wires,  by  v^,  v%,   .    .    .   vn,  the   instan- 
taneous potentials  of  the  points  on  the  various  wires  which  form 
the  terminals  of  the  absorbing  device,  and  by  i,  i%  .    .    .   in,  the 


POWER  MEASUREMENT  329 

instantaneous  currents  at  these  same  points.  Then  the  rate  of 
displacement  of  electricity  through  wire  No.  1  will  be  ii  and  the 
rate  of  doing  work,  or  the  instantaneous  power  will  be  iiVi,  and 
similarly  for  all  the  others.  Therefore, 

p  =  iiVi  +  izv2  +  .    .    .   invn  (a) 

In  practice  it  is  necessary  to  deal  with  potential  differences 
rather  than  with  potentials.  Let  IQ  be  the  potential  of  some 
particular  point  on  the  system.  In  general, 

i\  +  iz  +\i*  •    -    -   +  in  =  0 
consequently 

iiVo  +  izVo   .    .    .   +  ini'Q  =  0.  (b) 

Subtracting  (6)  from  (a) 

p  =  i\(vi  —  VQ)  +  iz(v2  —  VQ)    .    .    .   in(vn  —  v0). 
The  average  power  will  be 

i  r  i  CT 

P  =  TJ,  I     ii(vi  -  v0)dt  +    p  I     i2(v2  -  v0)dt 

Vn  ~  VQ}dt.    (26) 


\ 


i  r 

But  —  I    i  i(vi  —  Vo)dt,  etc.,  are  the  readings  of  the  n  wattmeters 

J-  Jo 

connected  as  above.  If  the  common  point  is  on  one  of  the  n 
wires  at  one  of  the  terminal  points  of  the  absorbing  device, 
then  one  of  the  quantities  in  parenthesis  will  be  zero,  the  cor- 
responding wattmeter  will  read  zero,  and  only  n  —  1  watt- 
meters will  be  required. 

The  above  demonstration  is  perfectly  general  and  therefore 
applies  in  all  cases  that  can  arise  in  polyphase  power  measure- 
ments. However,  the  consideration  of  the  cases  which  are  of 
frequent  occurrence  in  practice  is  instructive. 

Designation  of  Wattmeter  Terminals.  —  As  some  of  the  mean 
products  in  (26)  may  be  negative,  it  is  necessary  that  the  con- 
nections be  so  arranged  that  a  negative  deflection  of  the  watt- 
meter signifies  that  the  reading  should  be  subtracted  when  com- 
puting the  power.  That  there  may  be  no  confusion,  the  potential 
and  current  terminals  of  the  wattmeters  through  which  the  cur- 


330  ELECTRICAL  MEASUREMENTS 

rents  should  enter  when  flowing  from  the  generator  to  the  load 
should  be  determined  and  marked  on  the  instruments  once  for  all. 
The  proper  marking  may  be  determined  by  putting  the  instru- 
ments in  a  single-phase  circuit.  Then,  whenever  the  instruments 
are  used,  the  currents,  as  they  flow  from  the  generator  to  the 
load,  must  enter  both  the  current  and  the  potential  coils  at 
the  marked  terminals.  When  the  instruments  are  so  con- 
nected, if  the  pointer  deflects  up  the  scale,  the  mean  product  vi 
is  positive;  if  the  deflection  is  in  the  contrary  direction,  the  mean 
product  is  negative.  To  obtain  its  numerical  value  the  current 
coils  must  be  reversed,  and  the  reading  so  obtained  regarded 
as  negative.  This  simple  procedure  avoids  all  uncertainty  as 
to  the  algebraic  signs  of  the  readings  and  renders  unnecessary 
any  special  tests  for  their  determination.  The  terminals  of 
current  and  potential  transformers  should  be  similarly  marked. 

Two-phase  Three-wire  System. — By  the  theorem,  two  watt- 
meters are  required,  the  connections  being  as  in  Fig.  193. 


Load 


FIG.  193. — Power  measurement;  two-phase  three-wire  system. 


If  the  two  phases  are  separately  loaded,  it  is  obvious  that 
the  power  is  the  sum  of  the  wattmeter  readings.  A  load  might, 
however,  be  connected  between  leads  1  and  3  as  indicated  and 
then  the  instantaneous  power  would  be 

P    =    Vizi  12   +   023*23   +   Vziln 
V31    =    «>32   +   Vzi 
P    =    Vizi  12    +   023*23    +   032*31    +    021*31 

=  0i2(*i2  —  *si)  +  032(*3i  —  izs) 
ii  =  iiz  +  *i3  =  i\2  —  *'si 

is    =    *32   +   *31    =    *31    —    *23 

/.P  =  ~  f  vl2iidt  +  ~  I    vnitdt  (27) 

*  Jo  1  Jo 


POWER  MEASUREMENT 


331 


The  two  wattmeters  evaluate  the  integrals. 

Two  -wattmeter  Method.  —  Three-phase  system,  load  con- 
nected in  Y. 

By  BlondeFs  theorem  two  wattmeters  are  required.  Referring 
to  Fig.  194,  the  instantaneous  power  is 


p  = 


-f 


+ 


P    = 


i\  +  it  4-  fc's  =  0 

+   ^2o)    4"   izVZQ    4-   ia(VM   4- 

+  isVaz  +  (ii  +  iz  +  ^'3)^20 


i  r          i  r. 

.'.P  =  m]    tiVizdt  4-  ™  I    i&zzdt. 
i  Jo  ^  Jo 

The  two  integrals  are  given  by  the  wattmeters. 


(28) 


/!  -»-  i 


FIG.  194. — Power  measurement 
with  Y  load. 


FIG.  195. — Power  measurement 
with  A  load. 


A  A-connected  load  is  similarly  dealt  with. 

To  draw  the  vector  diagram  corresponding  to  Fig.  195,  assume 
that  the  load  is  balanced.  Let  Viz,  VM,  V3i  be  the  line  voltages 
and  6  the  phase  angle  between  the  potential  applied  to,  and  the 
current  in,  any  branch  of  the  circuit. 

From  the  figure  it  is  evident  that  instrument  No.  1  gives  the 
mean  product  of  the  instantaneous  value  of  Viz  and  7i  while  No. 
2  gives  the  same  product  for  Vsz  and  1^.  Using  the  effective 
values  of  line  voltage  and  line  current  (refer  to  Fig.  196)— 

Reading  of  No.  1  =  VI  cos  (30°  +  6)  =  VI  (-  sin  6  sin  30° 
+  cos  0  cos  30°) 


332 


ELECTRICAL  MEASUREMENTS 


Reading  of  No.  2  =•  VI  cos  (30°  -  0)  =  VI  (sin  6  sin  30° 
cos  B  cos  30°). 

Sum  of  No.  1  and  No.  2  =  VI  (2  cos  30°  cos  0) 

=  VI  \/3  cos  e  (29) 

which  is  the  power  applied  to  the  circuit. 

As  the  lag  angle,  0,  increases,  the  reading  of  No.  1,  which  is 
the  smaller  of  the  two,  decreases  and  will  become  zero  when 
6  =  60°  (corresponding  to  a  power  factor  of  0.5),  for  then 
and  Fi2  are  in  quadrature.  If  6  >  60°,  No.  1  will  reverse  and 


FIG.  196. — Vector  diagram  for  Fig.  195. 

its  reading  is  taken  as  negative  when  adding  the  readings  of 
No.  1  and  No.  2  to  obtain  the  power. 

It  will  be  noticed  that  the  phase  difference  of  F32  and  73  is 
the  same  as  that  of  Fi3  and  7i  and  as  the  maximum  values  of  the 
current  and  voltage  are  the  same  in  both  cases,  one  wattmeter 
will  suffice  for  measurements  on  a  balanced  load.  For  example, 
two  readings  may  be  taken  with  wattmeter  No.  1,  the  first  with 
the  potential  terminals  connected  between  mains  1  and  2,  the 
second  with  the  potential  terminals-  connected  between  mains  1 


POWER  MEASUREMENT  333 

and  3.  If  it  is  necessary  to  reverse  the  current  coils,  the  smaller 
of  the  readings  is  considered  negative. 

The  Polyphase  Wattmeter. — To  avoid  the  necessity  of  using 
two  separate  instruments  the  polyphase  wattmeter  has  been 
devised. 

The  instrument  consists  of  two  complete  wattmeters  mounted 
in  the  same  case.  The  two  movable  coils  are  attached  to  the 
same  rigid  stem  and  consequently  act  against  the  same  spring. 
The  deflection  is  thus  made  to  depend  on  the  sum  of  the  torques 
of  the  two  elements,  so  that  the  total  power  is  read  directly  from 
the  scale.  The  electrical  connections  are  the  same  as  for  two 
single-phase  wattmeters,  see  Fig.  194. 

Ample  insulation  must  be  provided  between  the  two  elements 
and  it  is  imperative  that  the  stray  field  from  one  element  have 
no  influence  on  the  torque  generated  by  the  other  element. 
'Protection  from  both  external  and  internal  stray  fields  may 
be  obtained  by  the  use  of  laminated  shields. 

In  careful  tests  at  low  power  factors  the  use  of  the  polyphase 
wattmeter  in  connection  with  instrument  transformers  is  to  be 
avoided,  for  the  necessary  corrections  for  the  ratio  and  phase 
angle  of  the  current  transformers  cannot  be  made. 

Fig.  197  shows  two  forms  of  polyphase  wattmeter.  The 
laboratory  instrument  is  read  by  means  of  a  torsion  head  and 
the  effect  of  the  stray  field  from  the  upper  element  on  the  torque 
of  the  lower  element  and  vice  versa  is  minimized  by  placing  the 
elements  with  their  axes  perpendicular. 

In  switchboard  instruments  the  interference  between  the 
elements,  which  would  naturally  be  large,  may  be  compensated 
by  an  ingenous  device  due  to  Edward  Weston.  Ordinarily  the 
potential  circuits  of  both  elements  of  a  polyphase  wattmeter 
are  connected  directly  to  lead  number  2  (see  Fig.  195).  Then, 
if  there  is  no  interference  and  the  resistance  of  each  potential 
circuit  is  n  +  r  ohms,  the  turning  moment  acting  on  the  mov- 
able system  is,  when  the  potential  coil  currents  are  in  and  2-32, 

K  rT  K  CT 

M  =  n,  I    iiiudt  +  ~  I    izizzdt  = 
2  Jo  J-  Jo 

(30) 


334  ELECTRICAL  MEASUREMENTS 


Weston  polyphase  switchboard  wattmeter. 


Drysdale  polyphase  wattmeter  for  laboratory  work. 
FIG.  197. 


POWER  MEASUREMENT 


335 


K  is  the  dynamometer  constant  for  each  of  the  two  elements. 
Equation  (30)  gives  the  correct  value  of  the  turning  moment. 

If  there  be  interference  between  the  elements,  and  K'  is  the 
constant  of  the  dynamometer  formed  by  the  lower  fixed  coil 
and  the  upper  movable  coil,  or  by  the  upper  fixed  coil  and  the 
lower  movable  coil,  the  turning  moment  is  modified  and  becomes 


K  CT  K'  CT  K  CT  Kf  CT 

'  =  m\    iiindt  +  Tp-  I    i&udt  +  ™  I    i&wdt  +  -^  \    iii 
1  Jo  1   Jo  1  Jj  -*  Jo 


M'  = 


(31) 


The    electrical    connections    for 
pensation  are  shown  in  Fig.  198. 


Weston's    method    of    com- 


FIG.  198. — Connections  for  compensating  a  polyphase  wattmeter  for 
interference  between  elements. 


The  compensation  is  effected  by  altering  the  potential  coil 
currents. 

This  is  done  by  causing  the  potential-coil  circuits  to  have  the 
part  TI  of  their  resistances  in  common.  The  currents  through 
the  potential  coils  then  become 


-f 


+  r) 


10    = 


and 


r(2n  + 

+  r)  — 


r) 


336 


ELECTRICAL  MEASUREMENTS 


When  the  potential  coil  currents  in  equation  (31)  are  replaced  by 
these  new  values  the  turning  moment  becomes 

K-fr,   -I-   r\    —    JT'r.  H      CT 

M'  = 


+ 


K'r  (~1     CT  1    CT 

L     t/0  J  0  J 

. _/rt_         ~T^      "I  ml     ilVatdt    +  Trr  I      izVizdt 


r(2fj  +  r) 

The  second  term  on   the    right-hand  side  disappears  if  n  is 
adjusted  so  that 

IT  = 


M'  then  reduces  to 


K 


M'  = 


That  is,  the  turning  moment  becomes  the  same  as  if  there  were 
no  interference.  If  the  instrument  is  of  the  deflectional  type 
the  correctness  of  this  adjustment  will  vary  for  different  points 
on  the  scale  but  the  error  will  be  small. 

The  present  practice  of  the  Weston  Instrument  Co.  is  to  use 
laminated  iron  shields  between  the  two  elements. 

Three-phase  Power  Measurement  by  Three  Wattmeters.— 
If  the  neutral  is  accessible,  the  sum  of  the  readings  of  three 
wattmeters  connected  as  in  Fig.  199  will  give  the  power. 


FIG.  199. — Connections  for  measurement  of  three-phase  power  by  three 

wattmeters. 

With  this  scheme  of  connections,  no  question  can  arise  as  to 
the  algebraic  sign  of  the  readings;  their  arithmetical  sum  gives 
the  desired  result. 


POWER  MEASUREMENT 


337 


It  is  not  necessary  that  the  neutral  be  accessible,  for  by  the 
theorem  one  has  only  to  connect  the  potential  coils  at  some 
common  point,  as  0'  in  Fig.  200. 


FIG.  200. — Connections  for  three-phase  power  measurements  with 
artificial  neutral. 


As  previously  shown 


but 


so 


-  T 

"rjo 

-  ^ 


1  CT  I  CT 

^Jo  *  Jo 

Vi2    —    ^10'   ~f"   ?'o'2 

^32  ==  VSQ'    i    VQ'-I 

1  r 

fTJ      I  \        ""  "      */ 

^  Jo 

1  r r   •      !  rr 

h  ^  ^30  ^3  «  +  -J^  ^o  2  ^J 


j   /T  j   /»r  !   /T 

P  =  -      uio't'iett  +  -  I    Wso'W^  +  -=,      Vzo'i 
^  Jo  ^  Jo  -L  Jo  - 

=  sum  of  wattmeter  readings. 


izdt 


(32) 


No  assumptions  are  made  as  to  the  resistances  of  the  potential 
circuits  of  the  wattmeters. 

If  the  load  is  balanced,  the  readings  on  all  three  instruments 
will  be  the  same;  this  leads  to  the  use  of  the  F-box  for  the 

measurement  of  balanced  three-phase  loads. 
22 


338 


ELECTRICAL  MEASUREMENTS 


The  Y-box. — The  F-box  consists  of  a  small  case,  like  that  of  an 
ordinary  multiplier,  containing  two  resistors  in  series,  both  oj 
which  have  a  resistance  equal  to  that  of  the  potential  circuit  of  the 
wattmeter  with  which  the  box  is  to  be  used.  As  a  tap  is  carried  to 
the  junction  of  the  two  resistors  the  F-box  has  three  terminals. 
It  is  connected  in  circuit  as  indicated  in  Fig.  201. 

If  the  load  is  balanced  the  power  is  given  by  P  =  3  times 
reading  of  wattmeter. 


FIG.  201.  —  Connections  of  F-box  for  measuring  three-phase  power  under 

balanced  loads. 

It  may  be  convenient  to  use  a  F-box  with  some  other  instru- 
ment than  that  for  which  it  was  designed;  in  this  case  the  factor 
is  no  longer  3.  Referring  to  Fig.  201,  by  KirchofFs  laws  the 
current  iv  through  the  potential  coil  of  the  wattmeter  is 

.         Viz  +  Vn 


where  Rv  is  the  resistance  of  the  potential  circuit  of  the  watt- 
meter and  r  is  the  resistance  of  each  section  of  the  F-box.  If  the 
line  current  be  iL  the  reading  of  the  wattmeter  is  given  by 


Therefore, 

Reading  = 


i  CT 

Rv-\    iviLdt. 
1Jo 


2Rv  +  r 
For  a  balanced  load  (see  page  332). 

power  =  -  |     iiv12dt+ 
2RV  +  r 


P  = 


K 


-££  ••>•«*+ IJ/ 

times  reading  of  wattmeter 


(33) 


POWER  MEASUREMENT 


339 


Four-wire  Three-phase  System. — The  power  will  be  given  by 
the  sum  of  the  readings  of  three  wattmeters  connected  between 
the  leads  1,  2,  3  and  the  neutral  point.  Fig.  202  shows  another 
arrangement  which  also  conforms  to  Blondel's  theorem. 


FIG.  202. — Connections  for  power  measurement  in  a  four-wire 
ohi 


three-phase  circuit. 


P 


[il    +   024*2   +   034*3 
but     Vi3    =    Vu   +   ^43 

023    =    024   +   043 

ii  +  iz  +  is  +  *4  =  0 

SO  P    =    (Vl3   +   034)^'l    +    (023   +   034^2   +    034(    ~    *'l    ~    *2    ~ 


^43^4^ 


i  r2    .        i  rr  i  r 

T7   V      0!3^1^f      I       ^   I      f23^2^t      '       ATT   I 

7  Jo  -t  Jo  J-  Jo 


(34) 


which  is  the  sum  of  the  readings  of  the  three  wattmeters.  The 
theorem  shows  that  the  power  in  any  four-  wire  combination  of 
loads  may  be  measured  by  three  wattmeters. 

References 

1.  "Compensating  Wattmeters,"  A.  L.  ELLIS,  Trans.  American  Institute 
of  Electrical  Engineers,  vol.  31,  1912,  p.  1579. 

2.  "On  the  Theory  of  Alternating  Current  Wattmeters,"  C.  V  DRYSDALE, 
The    Electrician,    vol.    46,    1900-1901,    p.    774.     "Wattmeter    Correcting 
Factors,"  C.  V.  DRYSDALE,  The  Electrician,  vol.  55,  1905,  p.  429,  p.  556, 
p.  676.     "The  Theory  of  the  Dynamometer  Wattmeter,"  C.  V.  DRYSDALE, 
Journal  Institution  of  Electrical  Engineers,  vol.  44,  1910,  p.  255. 

3.  "The  Compensated   Two-Circuit  Electrodynamometer,"  Edward  B. 
ROSA,  Bulletin  of  the  Bureau  of  Standards,  vol.  3,  1907,  p.  43.     "Compen- 


340  ELECTRICAL  MEASUREMENTS 

sated   Dynamometer  Wattmeter  Method  of  Measuring  Dielectric  Energy 
Loss,"  G.  B.  SHANKLIN,  General  Electric  Review,  vol.  19,  1916,  p.  842. 

4.  "The  Electrostatic  Wattmeter  in  Commercial  Measurements,"  MILES 
WALKER,  Trans.  American  Institute  of  Electrical  Engineers,  vol.  19,  1902,  p. 
1035.     "High-voltage  Tests  and  Energy  Losses  in  Insulating  Materials," 
E.  H.  RAYNER,  Journal  Institution  of  Electrical  Engineers,  vol.  49,  1912,  p.  3. 
At  the  end  of  this  paper  is  a  very  complete  bibliography  concerning  losses 
in  insulating  materials.     "Energy  Losses  in  Commercial  Insulating  Materials 
when  Subjected  to  High-potential  Stress,"  C.  E.  SKINNER,  Trans.  American 
Institute  of  Electrical  Engineers,  vol.  19,  1902,  p.  1047.*     "The  Use  of  the 
Electrostatic  Method  for  the  Measurement  of  Power,"  C.  C.  PATTERSON, 
E.  H.  RAYNER  and  A.  KINNES,  Journal  Institution  of  Electrical  Engineers, 
vol.  51,  1913,  p.  294.     "Ein  neues  Quadrantenelektrometer  fur  dynamisch 
Messungen,"  H.  SCHULTZE,  Zeit.  fur  Instrumentenkunde,  vol.  27,  1907,  p.  65. 

5.  "A  Power  Diagram  Indicator  for  High-tension  Circuits,"  HARRIS  J. 
RYAN,  Trans.  American  Institute  of  Electrical  Engineers,  vol.  30,  1911,  p. 
1089. 

6.  "An  Investigation  of  Dielectric  Losses  with  the  Cathode  Ray  Tube," 
JOHN  P.  MINTON,  Trans.  American  Institute  of  Electrical  Engineers,  vol.  34, 
1915,  p.  1627. 

7.  "Measurement  of  the  Energy  of  Polyphase  Currents,"  A.  BLONDEL, 
Proc.  International  Electrical  Congress,  Chicago,  1893,  p.  112. 

8.  "The    Double    Dynamometer    Wattmeter,"    C.    V.    DRYSDALE,    The 
Electrician,  vol.  76,  1916,  p.  523. 


CHAPTER  VII 

MEASUREMENT  OF  INDUCTANCE  AND  CAPACITY 

STANDARDS  OF  INDUCTANCE 

For  carrying  out  the  methods  of  measurement  described  in 
this  chapter,  standards  of  inductance  and  capacity  are  required, 
and  convenience  dictates  that,  in  many  cases,  they  be  made 
adjustable.  These  standards  may  be  divided  into  two  classes: 
primary  standards,  whose  values  are  calculated  from  their  di- 
mensions; and  secondary  standards,  whose  values  are  deter- 
mined experimentally. 

The  subject  of  the  calculation  of  primary  standards  of  self- 
and  mutual  inductance  is  beyond  the  scope  of  this  work.  Read- 
ers are  referred  to  the  papers  of  Rosa  and  Grover,  who  have  col- 
lected and  tested  all  the  available  formulae  and  have  published 
them  together  with  illustrative  examples  in  the  Bulletin  of  the 
Bureau  of  Standards.1 

Standards  of  Mutual  Inductance. — Primary  standards  of 
mutual  inductance  which  have  a  single  fixed  value  are  useful 
in  the  calibration  of  ballistic  galvanometers,  also  in  the  calibra- 
tion of  variable  working  standards  of  mutual  inductance  which 
are  used  in  the  laboratory. 

The  considerations  governing  the  design  are : 

1.  The  value  must  be  accurately  calculable  from  the  geo- 
metrical dimensions. 

2.  The  construction  must  be  such  that  permanence  is  assured. 

3.  The  value  must  be  sufficiently  large  to  give  high  sensitivity 
when  comparisons  are  made. 

4.  The  resistances  of  the  coils  must  be  kept  as  low  as  possible. 

5.  Eddy-current  effects  must  be  eliminated  as  far  as  possible. 

6.  The  capacity  effect  between  the  primary  and  the  secondary 
must  be  a  minimum. 

7.  The  bobbins  upon  which  the  coils  are  wound  must  be  free 
from  magnetic  materials. 

341 


342 


ELECTRICAL  MEASUREMENTS 


To  eliminate  eddy-current  effects,  all  conductors  which  carry 
large  currents  must  be  made  of  insulated  strands,  and  all  metal 
frames,  etc.,  near  the  coils  must  be  avoided. 

In  the  past  inductance  coils  have  frequently  been  wound  on 
bobbins  of  serpentine.  It  has  been  found,  however,  that  a  coil 
so  wound  has  an  inductance  which  depends,  to  a  slight  extent, 
upon  the  strength  of  current  flowing  in  the  conductor,  thus 
showing  that  the  permeability  of  serpentine  is  not  unity  and 
that  it  depends  on  the  magnetic  field  in  which  the  serpentine  is* 
placed. 


e 

c 

c 

Tl 

j          C 

Primary 

<-  -    -  -a—  —  >• 

I 

6 

i 

i 

4—  •   —10—  —->• 

Secondary 

cs 

I 

A                             •>. 

—  f  —  5 

: 

5          / 

r 

\  L 

c 

c 

c 
c 
c 

Primary 

T 

y 

\ 

FIG.  203. — Campbell  single  valued  primary  standard  of  mutual  inductance. 

For  primary  standards  of  self-inductance  it  is  customary  to 
use  single  layer  coils  which  are  wound  on  accurately  ground 
cylinders  of  marble,  or  of  plaster  of  paris  which  has  been  impreg- 
nated with  paraffin.  Such  a  construction  facilitates  the  exact 
determination  of  the  geometry  of  the  coil.  In  a  standard  of 
mutual  inductance,  this  construction  is  not  admissible  for  both 
the  primary  and  the  secondary  coils,  since  the  product  of  the 
primary  and  secondary  turns  must  be  large,  about  100,000 
for  a  mutual  inductance  of  0.01  henry. 

Campbell  Fixed  Standard  of  Mutual  Inductance.2 — It 
is  highly  desirable  that  the  arrangement  of  the  primary  and 
secondary  coils  in  a  standard  of  mutual  inductance  be  such  that 
errors  arising  from  slight  displacements  of  the  coils  from  their 
supposed  relative  position  will  be  reduced  to  a  minimum.  By 


INDUCTANCE  AND  CAPACITY 


348 


dividing  the  primary  into  two  equal  sections,  properly  separating 
them,  and  placing  the  secondary  midway  between  them,  all  three 
coils  being  coaxial,  a  satisfactory  arrangement  may  be  obtained. 
If  the  diameter  of  the  secondary  coil  is  such  that  the  mutual 
inductance  is  a  maximum,  the  secondary  will  be  so  placed  that 
its  circumference  is  in  a  zero  field.  For  this  reason  a  small  varia- 
tion in  the  diameter  or  a  small  axial  displacement  of  the  coil 
will  produce  only  a  slight  variation  in  the  mutual  inductance. 
The  construction  is  indicated  in  Fig.  203,  where  the  proper  rela- 
tive dimensions  are  shown. 

With  the  proportions  indicated  a  multiple  layer  secondary 
having  a  considerable  cross-section  (0.5  cm.  by  0.5  cm.)  may  be 
used.  The  effect  of  variations  of  the  diameter  of  the  secondary 
coil  are  shown  below.  The  mutual  inductance  is  a  maximum 
when  A  =  14.58  cm.  If  the  secondary  circuit  is  displaced  from 
the  midposition  between  the  primary  coils  by  0.35  cm.,  ra  is 
reduced  by  less  than  1  part  in  10,000. 

CAMPBELL  STANDARD  OP  MUTUAL  INDUCTANCE 
a  =  10  cm.,  6  =  7.5  cm.,  nin2  =  100,000 


A,  in  centimeters  

14.1 

14.3 

14.5 

14.7 

14.9 

15.0 

m,  in  millihenrys  

9.1630 

9.1728 

9.1759 

9.1759 

9.1696 

9.1567 

Variable  Mutual  Inductances. — Variable  mutual  inductances, 
in  other  words,  air  core  transformers  of  variable  ratio,  are  ex- 
tremely useful  in  alternating-current  measurements,  as,  for 
example,  in  determining  self-inductances  and  in  measuring  the 
ratios  of  instrument  transformers. 

For  the  highest  utility  the  coils  should  be  wound  astatically, 
expecially  if  the  apparatus  is  to  be  used  in  an  electrical  engineer- 
ing laboratory,  and  even  then  one  should  satisfy  himself  by  tests 
that  stray  field  effects,  due  to  non-uniform  fields,  are  absent. 
If  an  astatic  arrangement  is  not  used,  great  care  must  be  taken 
that  the  standard  is  not  set  up  where  there  are  alternating  stray 
fields  or  where  its  field  will  influence  other  instruments. 

It  is  desirable  that  the  scales  of  variable  mutual  inductances 
be  as  uniform  as  possible.  By  the  use  of  Lord  Rayleigh's  ar- 


344  ELECTRICAL  MEASUREMENTS 

rangement  of  two  concentric  circular  coils,  the  ratio  of  the  radii 
being  0.548  (see  page  80),  a  practically  uniform  scale  extend- 
ing over  about  60°  may  be  obtained;  if  the  coils  are  used  in  con- 
junction with  a  fixed  mutual  inductance  the  scale  may  be  ex- 
tended to  about  120°. 

Ayrton  and  Perry  Inductor.— The  Ayrton  and  Perry  variable 
standard  of  self-inductance  has  long  been  used  for  general  labora- 
tory purposes.  This  standard  consists  of  two  coils  of  slightly 
different  diameters,  the  smaller  pivoted  within  the  larger  in  such 


FIG.  204. — Ayrton  and  Perry  variable  inductor. 

a  manner  that  it  can  be  rotated  about  a  vertical  diameter.  The 
coils  are  connected  in  series  and  a  pointer  shows  their  relative 
position;  as  each  position  corresponds  to  a  particular  value  of 
the  self-inductance  of  the  combination,  the  dial  may  be  graduated 
in  henrys.  When  the  index  stands  at  the  lower  end  of  the  scale, 
the  inductance  of  the  combination  is  nearly  zero,  owing  to  the 
fact  that  the  currents  in  the  two  coils  are  circulating  in  opposite 
directions.  When  the  movable  coil  is  turned  through  90°,  the 
inductance  becomes  the  sum  of  the  self-inductances  of  the  two 
coils,  as  there  is  no  mutual  induction  in  this  position.  When 
turned  through  180°  the  currents  in  the  coils  are  in  the  same  di- 


INDUCTANCE  AND  CAPACITY  345 

rection  and  the  total  inductance  becomes  the  sum  of  the  self- 
inductances  of  the  coils  and  twice  their  mutual  inductance. 
Thus  the  inductance  of  the  standard  may  be  varied  continuously 
from  a  minimum,  which  is  nearly  zero,  to  a  maximum,  usually 
about  5  millihenrys.  The  scale  is  irregular  and  the  instrument 
is  not  astatic. 

Brooks  Variable  Inductor.3 — The  Brooks  Variable  Inductor 
very  closely  fulfills  the  requirements  for  a  variable  standard  of 
mutual  and  self-inductance.  It  was  developed  for  use  in  testing 
current  transformers  (see  page  581)  but  is  applicable  in  any 
measurement  where  such  a  variable  standard,  having  a  constant 
resistance,  is  necessary. 

The  particular  advantages  of  the  instrument  are  its  large 
carrying  capacity,  low  resistance  and  practically  uniform  scale. 
The  range  of  the  instrument,  as  described,  is  from  125  to  1,225 
microhenrys. 

Fig.  205  shows  the  instrument  complete  and  in  section,  as 
well  as  the  form  of  the  coils.  Referring  to  the  diagram  the  four 
coils,  F,  are  fixed ;  by  means  of  the  handle,  H,  the  two  movable 
coils,  M,  can  be  displaced  in  their  own  plane  about  the  axis,  A. 
The  number  of  flux  linkages  between  F  and  M  can  thus  be  varied. 
The  coils  of  stranded  wire  are  arranged  astatically.  Current  is 
carried  to  the  movable  coils  through  heavy  copper  spirals,  thus 
eliminating  all  contact  resistances.  The  cross  hatching  in  the 
diagram  indicates  the  numbers  of  turns  in  the  coils.  The  four 
fixed  coils  are  permanently  connected  in  series  and  provided 
with  binding  post  terminals;  likewise  the  two  movable  coils. 

When  the  fixed  and  movable  elements  are  connected  in  series 
the  instrument  may  be  used  as  a  standard  of  self-inductance,  and 
when  they  are  separated,  as  a  standard  of  mutual  inductance. 

The  self-inductance,  or  scale  reading,  is 

L  =  Li  +  L2  ±  2ra 

where  LI  and  L2  are  the  inductances  of  the  fixed  and  movable 
elements  and  m  is  the  mutual  inductance  of  the  elements.  LI 
and  L2are  constants,  and  for  the  instrument  as  described,  LI  +  L2 
=  669  microhenrys.  The  expression  for  the  mutual  inductance 
is  therefore 

L-^L^+JLt)  _  L  -  669 
±  m  ~  2  2 


346 


ELECTRICAL  MEASUREMENTS 


The  whole  device  is  about  14  in.  in  diameter.  The  interleaving 
of  the  fixed  and  movable  coils  is  important  for  if  M  recedes  axially 
from  one  fixed  coil  it  approaches  the  other,  so  that  the  net  effect 
on  the  inductance  of  a  slight  axial  displacement  of  M  is  zero. 


FIG.  205. — Brooks  variable  inductor. 

The  distinctive  feature  of  this  inductor  is  that  the  scale  divi- 
sions are  of  equal  length  throughout  the  greater  part  of  the  use- 


INDUCTANCE  AND  CAPACITY  347 

ful  range.  For  instance,  in  an  instrument  having  a  useful  range 
of  from  125  to  1,225  microhenrys  the  scale  is  uniformly  divided 
between  325  and  1,025  microhenrys;  outside  of  these  limits  the 
length  of  the  divisions  gradually  decreases,  but  there  are  no  sud- 
den changes. 

The  uniform  scale  is  attained  by  using  link-shaped  coils;  the 
proper  proportions  were  determined  experimentally  and  are 
given  below. 

Referring  to  Fig.  205 

r  =  mean  radius  of  semicircular  end  of  coil 

c  =  0.78r 

d  =  2.2r 
R  =  2.26r 
ri  =  O.Glr 
r2  =  1.39r       . 

The  net  cross-section  of  the  fixed  and  movable  coils  is  a  square 
having  a  side  c  units  long. 

STANDARDS  OF  CAPACITY 

As  examples  of  primary  standards  of  capacity,  that  is,  conden- 
sers whose  capacities  in  electrostatic  units  are  calculated  from 
their  dimensions,  those  used  by  Rosa  and  Dorsey4  in  their  de- 
termination of  Vj  the  ratio  of  the  electromagnetic  to  the  elec- 
trostatic unit  of  quantity,  may  be  taken.  It  is  in  connection 
with  the  determination  of  v  that  the  possible  sources  of  error 
in  such  primary  standards  have  been  most  carefully  studied. 

In  order  to  be  able  to  calculate  the  capacity  of  a  condenser 
with  a  high  degree  of  accuracy,  the  dielectric  coefficient  of  the 
medium  between  the  plates  must  be  definitely  known  and  the 
medium  must  be  free  from  absorption  and  from  dielectric  losses. 
For  these  reasons  air  is  always  used  as  the  dielectric  in  primary 
condensers.  Also,  the  distance  between  the  plates  must  be  so 
great  that  the  thickness  of  the  dielectric  may  be  determined  with 
accuracy.  In  consequence  of  these  facts  the  capacities  of  primary 
condensers  are  very  small. 

Three  forms  of  primary  condensers  have  been  developed,  viz., 
those  with  spherical,  cylindrical  and  plate  electrodes.  A  section 


348 


ELECTRICAL  MEASUREMENTS 


of  the  spherical  condenser  used  by  Rowland  in  the  determina- 
tion of  v  in  1879,  by  Rosa  in  1889,  and  by  Rosa  and  Dorsey  in 
1905,  is  shown  in  Fig.  206. 

The  capacity  in  electrostatic  units  of  such  a  spherical  air  con- 
denser is 

Rr 


where  R  and  r  are  the  radii  bounding  the  dielectric. 


FIG.  206. — Section  of  spherical  air  condenser. 

The  internal  radius  of  the  spherical  shell  in  the  Rowland  con- 
denser is  12.67158  cm.,  and  the  radius  of  the  ball  is  10.11806  cm. 
(at  20°).  The  capacity  is,  therefore,  50.2095  electrostatic  units. 

When  the  condenser  is  used,  the  ball  must  be  carefully  centered 
and  corrections  made  for  the  holes  in  the  shell,  the  bushings,  and 
the  cord  by  which  the  ball  is  suspended.  The  error  in  the  final 
calculated  value  of  the  capacity  was  estimated  at  about  2  parts  in 
100,000.  When  measured  by  Maxwell's  method  (see  page  362) 
the  capacity  was  found  to  be  5.59328X10~20  absolute  electro- 
magnetic units  or  0.0000559328  microfarad. 


INDUCTANCE  AND  CAPACITY 


349 


In  any  experimental  work  with  such  a  very  small  capacity,  it 
is  necessary  to  make  allowances  for  the  capacity  of  the  wire  by 
which  the  charge  is  imparted  to  the  ball,  for  the  capacity  of  all 
leads  and  of  the  commutator  by  which  the  charging  and  dis- 
charging is  effected. 

The   capacity  of  an   air   condenser  with   coaxial   cylindrical 
electrodes,    if   the   charge   be  uni- 
formly   distributed,    is    given    in 
electrostatic  units  by 


C  =  — 


where  I  is  the  length  of  the  cylin- 
der and  R  and  r  are  the  radii 
bounding  the  dielectric.  For  pre- 
cision work,  on  account  of  the 
effect  of  the  ends  of  the  condenser, 
the  assumption  of  a  uniform  den- 
sity of  charge  is  not  tenable,  so  re- 
course is  had  to  guard  cylinders, 
shown  in  Fig.  207  at  G.  The  effect 
of  the  ends  is  thus  removed  from 
the  central  section,  which  is  the 

one  connected   to  the    measuring     ,  .Fl(?-  .207.— Section   of  cylin- 
drical air  condenser  with  guard 
apparatus,  to  the  guard  cylinders    cylinders. 

where  it  does  no  harm.     In  order 

to  make  practically  all  the  lines  of  force  radial  the  air  gaps  be- 
tween the  main  section  and  the  guard  cylinders  must  be  made 
as  small  as  possible,  and  the  measuring  apparatus  so  arranged 
that  the  guard  cylinders  are  always  at  the  same  potential  as 
the  main  or  central  section. 

For  one  of  the  condensers  used  by  Rosa  and  Dorsey, 

I  =  20.00768  cm. 

R  =    7.23831  cm. 

r  =    6.25740  cm. 


Then,  as  a  first  approximation,  C 
electrostatic  units. 


20.00769 


2  log. 


7.3831 
6.25740 


=  68.696 


350  ELECTRICAL  MEASUREMENTS 

This  result  must  be  corrected  for  the  effects  of  the  gaps  between 
the  main  cylinder  and  the  guard  cylinders  and  for  the  different 
thicknesses  of  the  dielectric  on  the  two  sides  of  the  gaps  due  to 
differences  in  the  diameters  of  the  cylinders.  The  deduction  of 
these  corrections  involves  the  use  of  the  higher  forms  of  analysis. 
The  numerical  value  of  the  net  correction  for  the  condenser  just 
mentioned,  when  the  lower  gap  is  0.6  mm.  and  the  upper  gap 
0.5  mm.,  is  +0.182  electrostatic  units.  Thus,  in  the  case  of  this 
short  condenser,  the  corrections  with  even  these  small  air  gaps 
amount  to  over  one-fourth  of  1  per  cent.  The  longer  the  central 
section,  the  smaller  is  the  percentage  correction. 

For  the  most  refined  work  the  parallel  plate  condenser  is 
inferior  to  these  just  referred  to,  for  comparatively  large  errors 
may  be  introduced  if  the  adjustments  are  not  perfect. 

Secondary  Air  Condensers. — Secondary  air  condensers  are 
useful  in  experimental  work  in  those  cases  where  the  dielectric 
losses  must  be  reduced  to  zero;  as  "in  determining  the  phase 
angles  of  mica  condensers  or  in  the  investigation  of  the  dielectric 
losses  occurring  in  insulating  materials.  As  such  condensers 
must  be  calibrated,  it  is  possible  to  use  for  each  electrode  a  num- 
ber of  plates  in  parallel  and  to  make  the  distance  between  the 
electrodes  only  a  few  millimeters.  By  this  means  capacities 
of  a  few  hundredths  of  a  microfarad  may  be  obtained  without 
undue  bulk. 

In  any  air  condenser,  the  ohmic  resistance  between  the  termi- 
nals and  the  condenser  proper  must  be  kept  low  in  order  that 
there  may  be  no  appreciable  internal  PR  losses  which  would 
cause  an  alternating  current  to  lead  the  applied  voltage  by  less 
than  90°. 

A  secondary  air  condenser,5  having  a  capacity  of  0.01 
microfarad,  is  shown  (with  the  case  removed)  in  Fig.  208,  A. 
The  plates  (of  magnalium)  are  20  cm.  in  diameter,  1  mm.  thick, 
and  so  spaced  that  the  thickness  of  the  dielectric  is  2  mm.;  35 
plates  are  used  in  one  electrode  and  36  in  the  other.  In  order 
to  insure  permanence  a  very  solid  construction  must  be  employed. 

The  plates  are  supported  as  shown  in  Fig.  208,  B.  The  bronze 
ring,  Rij  is  firmly  screwed  to  the  base  of  the  instrument;  through 
it  pass  four  adjusting  screws  of  fine  pitch,  Q,  which  support  a 
second  ring,  R2,  by  means  of  the  little  amber  cylinders,  B,  which 


INDUCTANCE  AND  CAPACITY 


351 


move  in  the  guides,  r.  Four  equally  spaced  brass  rods,  5  mm. 
in  diameter  and  having  screw  threads  cut  on  their  upper  ends, 
are  firmly  attached  to  ring  R  i}  and  pass  upward,  with  ample 
clearances,  through  holes  in  the  ring  R2.  Four  equally  spaced 
vertical  rods  are  attached  to  7?2.  Each  plate  is  pierced  with 
eight  holes,  four  of  them  5  mm.  and  four  12  mm.  in  diameter. 
The  holes  are  so  placed  that  they  accommodate  the  eight  vertical 
rods. 


A  B 

FIG.  208. — Secondary  air  condenser. 

The  condenser  is  built  up  by  first  putting  on  a  member  of 
electrode  2.  The  smaller  holes  in  this  plate  just  fit  the  rods 
Sz  and  the  larger  holes  allow  ample  clearances  for  the  rods  Si. 
Distance  pieces  of  the  proper  diameter  and  of  a  length  sufficient 
to  give  a  2-mm.  air  space  between  the  plates  are  then  slipped 
over  the  rods  Si.  They  rest  on  the  ring  Ri  and  pass  with  ample 
clearances  through  the  holes  in  R2',  on  these  four  distance  pieces 
rests  the  first  plate  of  electrode  1.  Distance  pieces  8  mm.  in 
diameter  and  5  mm.  long  are  then  slipped  over  the  rods  $2  and 
rest  on  top  of  the  first  plate  of  electrode  2;  the  second  plate  of 
electrode  2  is  then  slipped  on  and  rests  on  the  top  of  the  distance 
pieces,  and  so  on. 


352  ELECTRICAL  MEASUREMENTS 

When  the  pile  has  been  completed,  electrode  1  is  firmly  clamped 
between  the  rings  R\R\  by  means  of  the  nuts  M.  Electrode 
2  is  clamped  between  the  rings  R2R2.  The  spaces  between  the 
two  electrodes  are  finally  adjusted  by  raising  or  lowering  electrode 
2  by  means  of  the  adjusting  screws  Q,  which  are  then  locked. 
The  top  of  2  is  firmly  held  by  tightening  and  then  locking  the 
screws  N  which  bear  on  the  ring  R2  by  means  of  the  amber 
cylinders  B. 

The  assembled  condenser  is  about  30  cm.  high  and  weighs 
approximately  37J/2  lb. 

By  making  the  air  spaee  1  mm.  instead  of  2  mm.  and  employing 
107  plates,  condensers  having  a  capacity  of  0.03  microfarad 
have  been  constructed.  With  this  extremely  small  thickness 
of  the  dielectric,  trouble  was  experienced  in  insulating  the  two 
sets  of  plates,  for  when  voltage  was  applied  fine  particles  of  dust 
from  the  air  bridged  the  space  between  the  plates,  thus  reducing 
the  insulation  resistance.  It  is  not  possible  to  remove  the 
dust  after  the  condenser  is  assembled  but  the  insulation  may 
be  improved  by  placing  a  drying  material  in  the  case  of  the 
instrument. 

The  breakdown  voltage  of  the  condenser  with  2  mm.  air  space 
is  3,000  volts,  and  with  1  mm.  air  space,  900  volts.  All  sharp 
edges  on  the  plates  and  internal  fittings  must  be  avoided,  in 
order  to  prevent  brush  discharges. 

To  render  the  condenser  independent  of  the  surroundings,  one 
set  of  plates  is  connected  to  the  case,  the  other  set  being  con- 
nected directly  to  the  measuring  apparatus. 

Variable  capacities  are  necessary  for  general  laboratory  pur- 
poses, but  a  difficulty  presents  itself  when  one  attempts  to  put 
a  number  of  very  small  condensers  in  parallel  by  the  ordinary 
means,  since  the  connections  possess  an  unknown  capacity  which 
may  be  enough  to  introduce  serious  errors.  For  this  reason  it 
is  necessary  that  the  design  of  the  small  sections  from  which  the 
larger  capacities  are  built  up  be  such  that  this  uncertainty  is 
eliminated.6 

In  the  most  refined  work  the  temperature  coefficient  of  an 
air  condenser,  due  to  the  change  of  dimensions  and  change  in 
the  dielectric  coefficient  of  the  air,  must  be  considered.  It- 
may  amount  per  degree  to  2  or  3  parts  in  100,000. 


INDUCTANCE  AND  CAPACITY 


353 


The  dielectric  strength  of  air  condensers  may  be  greatly 
increased  if  the  dielectric  be  dry  compressed  air,  at.  a  pressure 
of  60  Ib.  per  square  inch  or  greater.7  This  eliminates  brush 
discharges  and  energy  losses  at  high  voltages.  For  example, 
with  an  air  pressure  of  175  Ib.  per  square  inch,  a  condenser  with 
plates  2.1  mm.  apart  showed  no  appreciable  energy  loss  at  27,500 
volts.  It  broke  down  at  28,500  volts. 

In  another  case  with  the  plates  3.2  mm.  apart  the  break- 
down voltage  at  atmospheric  pressure  was  6,000  volts ;  when  the 


FIG.  209. — Compressed  gas  condenser  for  use  in  radio-telegraphy. 

air  pressure  was  raised  to  260  Ib.  per  square  inch  the  break- 
down voltage  became  30,000. 

It  is  necessary  to  use  a  drying  material  in  the  condenser  cases. 
The  use  of  compressed  air,  of  course,  necessitates  a  strong  and, 
therefore,  a  very  heavy  metal  case.  A  practical  difficulty  arises 
in  the  introduction  of  the  lead  to  the  insulated  set  of  plates; 
it  must  be  perfectly  insulated  and  all  joints  must  be  air-tight 
as  well.  Practically,  the  casing  cannot  be  made  absolutely 

23 


354 


ELECTRICAL  MEASUREMENTS 


tight,  so  a  pressure  gage  must  be  supplied  and  the  air  pressure 
renewed  from  time  to  time. 

Experience  has  shown  that  with  careful  construction  the 
pressure  may  not  fall  more  than  20  Ib.  during  a  year  from  an 
initial  value  of  220  Ib.  per  square  inch. 

Compressed  gas  condensers  are  used  in  connection  with  radio- 
telegraphic  apparatus.  Fig.  209  shows  one  of  those  installed 
at  Arlington,  Va.,  by  the  United  States  Government. 

Working  Standards  of  Capacity. — Though  the  determination 
of  the  capacity  and  phase  angle  of  working  standards  of  capa- 


.05 


.05 


Microfarads 


B 
FIG.  210. — Subdivided  condenser. 

city  depends  ultimately  upon  the  use  of  secondary  air  condensers, 
such  instruments  are  not  suitable  for  general  use  in  the  labora- 
tory on  account  of  their  size,  and  more  convenient  arrangements 
must  be  employed.  Ordinarily  the  capacity  of  laboratory 
standards  is  of  the  order  of  magnitude  1  microfarad.  Such 
standards  should  be  subdivided  and  made  adjustable  by  arrange- 
ments for  placing  the  various  sections  in  parallel.  When  this  is 
done  the  net  capacity  in  terms  of  the  capacities  of  the  various' 
sections  is 

C  =  Ci  +  C2  +  C3  + . . . . 


x         INDUCTANCE  AND  CAPACITY  355 

The  usual  construction  of  the  terminal  blocks  for  putting  the 
sections  in  parallel  is  shown  in  Fig.  210.  By  the  proper  insertion 
of  the  plugs,  the  sections  may  'be  put  in  parallel  as  desired,  any 
section  may  be  discharged,  or  the  whole  condenser  may  be 
short-circuited. 

For  precision  standards  of  small  capacity,  this  scheme  of 
connections  is  open  to  the  objection  that  the  capacity  of  the  top 
itself,  which  depends  upon  the  position  of  the  plugs,  is  included 
between  the  terminals.  For  precision  work,  it  is  better  to  have 
each  section  provided  with  small  and  well-insulated  terminal 


FIG.  211. — Subdivided  precision  condenser. 

posts,  spaced  as  far  apart  as  practicable.     This  also  allows  the 
sections  to  be  connected  in  series  as  well  as  in  parallel. 
With  the  series  connection  the  capacity  will  be 


C  = 


C\ 


The  capacity  in  electrostatic  units  of  a  condenser  with  parallel 
plates  separated  by  a  medium  having  a  dielectric  coefficient 
Kis 


356  ELECTRICAL  MEASUREMENTS 

A  is  the  total  active  area  of  one  set  of  plates  and  t  is  the  thick- 
ness of  the  dielectric. 

To  transfer  the  value  of  the  capacity  from  the  electrostatic 
to  the  electromagnetic  system  of  units, 

v  =  2.996  X  1010 
v*  =  8.976  X  1020. 

One  c.g.s.  electromagnetic  unit  of  capacity  =  v2  c.g.s.  electro- 
static units  of  capacity. 

One  c.g.s  electromagnetic  unit  of  capacity  =  10 15  microfarads. 
Consequently  the  capacity  in  microfarads  of  a  parallel  plate 
condenser  is 

KAIO15  Q.8S6KA 

(2.996  X  1010)2  4irt   ~~          IWt      ' 

Obviously,  to  increase  the  capacity  without  an  undue  increase 
of  bulk,  a  dielectric  having  a  high  dielectric  coefficient  and  capable 
of  being  used  in  very  thin  sheets  must  be  employed.  The 
material  chosen  should  have  an  exceedingly  high  specific  resistance 
and  high  dielectric  strength. 

The  above  formula  for  capacity  is  convenient  for  rough  pre- 
liminary calculations;  as  t  cannot  be  known  with  any  great 
certainty  all  condensers  with  dielectrics  of  small  thickness  must 
be  calibrated. 

All  materials  used  in  the  construction  of  condensers  must  be 
clean  and  perfectly  dry  and  the  finished  instrument  must  be 
sealed  in  some  manner  so  that  the  access  of  moisture  is  prevented. 
Mica  and  paraffined  paper  are  the  materials  commonly  used 
for  the  dielectric.  Air  pockets  in  the  dielectric  must  be  entirely 
eliminated. 

Temperature  has  an  appreciable  effect  on  the  behavior  of 
condensers  having  solid  dielectrics.  It  is  not  possible  to  give 
a  definite  statement  as  to.  the  temperature  coefficient  of  the 
capacity  of  a  particular  condenser,  for  the  temperature  effects 
are  dependent  on  the  particular  cycle  of  operations  to  which 
the  condenser  is  subjected.  This  is  illustrated  in  Figs.  212A  and 
2125,  which  are  typical  of  good  and  poor  mica  condensers.  The 
best  mica  condensers  when  subject  to  the  ordinary  fluctuations 
of  room  temperature  may  show  variations  in  the  capacity  of  2 
or  3  parts  in  10,000. 


INDUCTANCE  AND  CAPACITY  357 

The  active  portion  of  any  condenser  intended  for  use  as  a 
standard  must  be  firmly  confined  between  clamps,  so  that  its 
geometry  and,  consequently,  the  capacity  of  the  condenser  may 
be  definite.  Condensers  without  clamps  are  greatly  affected  by 
temperature,  and  when  taken  through  a  cyclic  variation  of 
temperature  (for  instance,  17°,  30°,  17°),  do  not  return  to  their 
initial  capacities.  This  permanent  alteration  may  be  as  much 
as  3  or  4  parts  in  10,000. 

Condensers  on  Direct-current  Circuits. — In  the  use  of  conden- 
sers with  direct  currents,  difficulties  arise  from  "absorption" 
and  its  related  effects.  It  is  found  that  the  discharge  of  any 
condenser  having  a  solid  dielectric  consists  of  two  portions— 
a  sudden  rush  of  current  at  the  instant  of  closing  the  circuit, 
due  to  the  free  charge,  and  a  small,  gradually  decreasing  current, 
due  to  the  liberation  of  the  "absorbed"  charge.  This  latter 
current  complicates  the  various  methods  of  measurement  when 
direct  currents  are  employed  (see  "Direct-deflection  Method," 
page  369).  If  high  voltages  be  used,  the  absorbed  charge  con- 
tinues to  be  given  up  for  a  long  time. 

When  the  condenser  is  charged,  the  first  rush  of  current 
consists  of  two  portions — one  furnishing  the  free  charge,  the 
second  a  diminishing  current  furnishing  the  absorbed  charge. 
This  latter  current,  for  a  short  time,  about  0.01  sec.,  may  be  rela- 
tively large.  If  the  charging  circuit  be  broken  too  soon,  before 
the  dielectric  is  "saturated,"  the  absorption  goes  on,  and  if  there 
is  a  delay  in  discharging  the  condenser,  the  free  charge  will  be 
diminished  below  its  proper  value.  Thus  the  apparent  capacity 
depends  on  the  previous  history  of  the  condenser,  on  the 
time  of  charging,  on  the  length  of  time  between  disconnecting 
from  the  battery  and  discharging  and  on  the  time  of  discharge. 

An  arbitrary  measure  of  the  absorption  may  be  obtained  by 
subjecting  the  condenser  to  a  definite  series  of  operations,  for 
example,  by  charging  for  1  sec.,  insulating  for  30  sec.,  discharging 
instantaneously  through  a  ballistic  galvanometer,  insulating 
for  30  sec.,  discharging  again,  and  so  on,  until  five  residual  de- 
flections have  been  obtained.  The  measure  of  the  absorption 
is  the  total  quantity  in  the  five  residuals  expressed  as  a  fraction 
of  the  free  charge.  The  absorption  curves  in  Fig.  212  were 
obtained  in  this  manner. 


358  ELECTRICAL  MEASUREMENTS 

As  the  absorption  increases  very  markedly  with  the  increase 
in  temperature,  while  the  insulation  resistance  decreases,  con- 
densers are  preferably  used  at  low  temperatures,  about  20°. 

The  measured  capacities  of  condensers  which  have  large 
absorption  are  greatly  affected  by  the  time  of  discharge. 

Condensers  on  Alternating-current  Circuits. — If  an  air  con- 
denser, which  is  perfectly  insulated  and  the  resistance  of  whose 
leads  is  zero,  is  subjected  to  an  alternating  potential  difference, 
the  current  flowing  into  the  condenser  will  lead  the  potential 
difference  across  its  terminals  by  90°,  there  being  no  expenditure 
of  energy;  if  the  dielectric  is  solid,  energy  is  expended  in  the  con- 
denser as  is  shown  by  its  rise  of  temperature  under  continuous 
operation.  If  energy  is  expended,  the  current  flowing  into  the 
condenser  must  have  an  energy  component,  or,  in  other  words, 
the  current  and  potential  difference  will  no  longer  have  a  phase 
difference  of  90°.  The  amount  of  departure  from  the  90°  rela- 
tion will  be  denoted  by  <j>:  the  power  factor  of  the  condenser  is 
then  sin  <f>.  The  angle  <£,  called  the  phase  angle,  is  dependent 
on  the  quality  of  the  condenser.  For  a  first-class  instrument  with 
mica  as  the  dielectric,  it  may  not  be  more  than  a  few  minutes  of 
arc,  possibly  5,  and  may  be  much  below  this.  If  the  condenser 
is  of  poor  quality  with  a  paraffined  paper  dielectric,  this  angle 
may  in  extreme  cases  be  as  much  as  20°.  The  power  factor  of 
such  inferior  condensers  is  very  sensitive  to  changes  of  frequency. 
It  must  not  be  assumed  that  mica  condensers  are  of  necessity 
characterized  by  very  small  phase  angles,  for  such  condensers 
from  well-known  makers  may  occasionally  show  phase  angles  of 
several  degrees.  Such  abnormal  values  are  found  most  frequently 
in  the  small  sections  (Hooo  microfarad)  and  show  the  condenser 
to  be  of  poor  quality.  In  a  divided  condenser,  the  different 
sections  may  have  very  different  phase  angles.  The  measured 
capacities  of  condensers  which  have  large  phase  angles  will  be 
found  to  be  very  dependent  on  the  frequency. 

Various  methods  for  the  measurement  of  electrostatic  capacity 
by  means  of  alternating  currents  are  to  be  given  and  it  is  of  prac- 
tical importance  to  be  able  to  apply  them  to  condensers  with  im- 
perfect dielectrics  such  as  are  met  with  in  practice,  that  is,  to  find 
the  equivalent  capacity  of  such  condensers.  As  there  is  a  dissi- 
pation of  energy  in  the  condenser,  its  equivalent  arrangement 


INDUCTANCE  AND  CAPACITY 


359 


should  be  a  perfect  condenser  in  connection  with  such  a  resistance 
that  the  energy  dissipated  in  the  combination  is  the  same  as  that 
in  the  actual  condenser.  The  energy  loss  may  be  duplicated  by 
assuming  the  resistance  to  be  either  in  parallel  or  in  series  with 
the  perfect  condenser,  as  is  indicated  below. 

Given  V,  I,  P,  co,  and  assuming  sinusoidal  currents, 


rrangement 


Parallel  Arrangement 


P  =  Prs 


•  rs  = 


tan  6  =  — 77-  leading 


P  = 


ZP  = 


72 


72 


tan  6  =  cofpCp  leading 
Power  factor  =  P.F.  =  cos  6 
Phase  angle,  <£  =  tan"1  corsCs     Phase  angle,  <f>  =  tan"1  - 

Cs     =  TT  -*     r  a  ^v  1 


-  p.F. 


To  illustrate  the  foregoing  the  following  measurements  of  a 
5-mile  length  of  impregnated  paper  cable  used  in  power  trans- 
mission may  be  taken. 

Applied  P.D 30,000  volts. 

Current 10  amp. 

Power  supplied  to  cable 12,000  watts. 

Cycles  per  second 60 

From  these  data : 

Power  factor  =  ^oo°)< To  =  °-°4 

Power-factor  angle  =  87°71,  denoted  by  6. 

Phase  angle  =  90°  -  87°71  =  2°29,  denoted  by  tf>. 


360  ELECTRICAL  MEASUREMENTS 

Then 

rs  =  120  ohms  rp  =  75,000  ohms 

leakance  =  0.0000133  + 
Cs  =  0.8848  microfarad  CP  =  0.8835  microfarad 

In  cases  where  the  dielectric  losses  are  large,  the  equivalent 
capacities  for  the  series  and  the  parallel  arrangements  are  slightly 
different. 

The  equivalent  parallel  resistance  rP  has  no  relation  to  the 
insulation  resistance  as  measured  with  direct  current. 

Mica  Condensers. — Mica  is  used  as  the  dielectric  in  the  best 
working  standards  of  capacity.  Its  specific  resistance  is  about 
1  X  1010  (megohm,  centimeter).  Its  dielectric  coefficient 
varies  between  6  and  8.  The  puncturing  voltage  of  selected 
specimens  0.1  mm.  thick,  when  tested  between  plates  may  be 
as  high  as  12,000  volts  (r.m.s.).  The  average  strength  is  much 
lower. 

Mica  condensers  are  not  ideally  perfect  and  vary  greatly  in 
their  properties,  so  that  in  careful  work  the  characteristics  of 
the  particular  condenser  employed  as  a  standard  must  be  known. 
However,  a  mica  condenser  always  behaves  in  the  same  manner 
if  the  same  conditions  be  maintained.  For  this  reason,  in  work 
of  high  precision,  the  cycle  of  operations  to  which  the  condenser 
is  subjected,  both  when  its  capacity  is  determined  and  in  sub- 
sequent use,  should  be  the  same.  The  capacity  of  a  good  mica 
condenser  is  independent  of  the  voltage. 

To  be  useful  as  a  standard  a  mica  condenser  must  be  firmly 
clamped. 

Experiments  show  that  the  capacity  of  a  good  mica  con- 
denser, when  determined  at  higher  and  higher  frequencies  by  a 
method  of  rapid  charge  and  discharge  using  direct  currents, 
approaches  the  same  value  as  that  obtained  by  the  use  of  alter- 
nating currents,  the  period  with  alternating  currents  and  the 
time  of  discharge  with  direct  currents  being  the  same.  The  two 
curves  connecting  the  reciprocal  of  the  frequency  and  the  capa- 
city and  the  time  of  discharge  and  the  capacity,  when  extrapo- 
lated for  infinite  frequency  and  zero  time  of  discharge  apparently 
cut  the  capacity  axis  at  the  same  point.  The  capacity  determined 
by  this  process  of  extrapolation  is  called  the  " instantaneous," 
or  by  some  writers,  the  " geometric"  capacity,  being  independent 


INDUCTANCE  AND  CAPACITY 


361 


of  absorption  and  depending  only  on  the  dielectric  coefficient  and 
on  the  dimensions  of  the  condenser. 

Changes  of  atmospheric  pressure  cause  minute  changes  of 
capacity  in  mica  condensers  which  may  be  detected  by  the  most 
refined  methods  of  measurement.  The  changes  are  subject  to 
a  considerable  time  lag  and  may  be  of  the  order  of  magnitude, 
1  or  2  parts  in  100,000  for  1  cm.  change  of  pressure.  Usually 
if  the  pressure  be  reduced,  the  condenser  expands  and  as  the 
increase  in  the  distance  between  the  plates  produces  more  effect 


O.OUOGmf. 


"  Tempera 


"  Temperature 


A  \B 

FIG.  212. — Characteristics  of  good  (A)  and  poor  (B)  mica  condensers. 

than  their  increase  of  size,  the  capacity  is  decreased.  Firmly 
clamped  condensers  are  but  very  slightly  affected. 

The  characteristics  of  good  and  poor  mica  condensers  are 
illustrated  by  Fig.  212. 

Condensers  of  silvered  mica  are  sometimes  used,  but  are  in- 
ferior to  those  of  the  ordinary  construction,  being  more  unstable 
and  having  a  capacity  dependent  upon  the  voltage.  This  un- 
stable character  is  probably  due  to  deposits  of  silver,  under  flakes 
of  mica,  which  are  imperfectly  attached  to  the  main  deposit. 


362 


ELECTRICAL  MEASUREMENTS 


INDUCTANCE  AND  CAPACITY 


363 


S   3 


364  ELECTRICAL  MEASUREMENTS 

Paraffined  Paper  Condensers.9 — On  account  of  the  possibility 
of  large  absorption  effects  and  frequency  errors,  paraffined 
paper  condensers  should  not  be  employed  as  standards.  No 
general  rule  concerning  their  behavior  can  be  formulated.  When 
used  with  alternating  current,  the  capacity  of  a  paraffined  paper 
condenser  decreases  with  an  increase  of  frequency  and  very 
markedly  if  the  phase  angle  be  large.  An  increase  of  tempera- 
ture usually  causes  an  increase  in  the  capacity;  for  an  exception 
see  Fig.  213.  The  phase  angle  is  much  larger  than  that  of  a  good 
mica  condenser.  It  generally  increases  with  a  rise  of  tempera- 
ture and  more  and  more  rapidly  as  the  temperature  becomes 
higher.  The  phase  angle  is  very  susceptible  to  changes  in  fre- 
quency. Usually  an  increase  of  frequency  causes  a  decrease  in 
the  angle.  Fig.  213  shows  the  characteristics  of  a  good  paraffined 
paper  condenser.  Fig.  214  applies  to  a  rolled  condenser  such  as  is 
frequently  used  in  telephony,  and  an  inspection  of  the  curves 
will  show  that  this  is  a  poor  instrument  and  that  in  some  respects 
its  behavior  is  the  reverse  of  that  of  the  better  condenser. 

The  internal  resistance  of  a  condenser,  that  is,  the  resistance 
of  the  connections  from  the  binding  posts  to  the  plates  and  of 
the  plates  themselves,  may  cause  an  abnormal  phase  angle.  This 
is  the  case  in  that  form  of  telephone  condenser  which  is  made  by 
rolling  up  long  strips  of  tin  foil  together  with  the  paper  dielectric, 
the  electrical  connections  being  made  at  the  ends  of  the  strips. 
High  internal  resistance  causes  excessive  heating  and  an  increase 
of  phase  angle  with  an  increase  of  frequency. 

METHODS  OF  MEASUREMENT 

Determination  of  Capacity  in  Absolute  Measure. — Maxwell  in 
his  " Treatise  on  Electricity  and  Magnetism"*  gives  a  bridge 
method  for  determining  the  electrostatic  capacity  of  a  condenser 
in  electromagnetic  measure.  This  method  has  been  employed 
in  many  determinations  of  "v"  and  is  probably  the  best  yet 
devised  for  determining  pure  capacities  in  absolute  measure.4 
The  connections  are  shown  in  Fig.  215. 

The  condenser  to  be  measured  is  at  C;  M,  N,  and  P  are  the 
resistances  of  the  bridges  arms,  B  is  the  battery  resistance  and 

*Art.  776,  third  edition. 


INDUCTANCE  AND  CAPACITY 


365 


RG  and  LG  the  resistance  and  self-inductance  of  the  galvanometer. 
The  resistances  ab  and  cd  are  negligibly  small.  The  condenser 
is  rapidly  charged  and  discharged  by  the  switch  e,  which  is  usually 
a  commutator  driven  at  a  constant  and  known  speed. 

When  contact  is  made  at  c,  the  condenser  is  discharged  and  so 
remains  until  the  tongue  e  touches  b.  Until  e  touches  b  the  cur- 
rents in  the  network  are  determined  by  the  e.m.f.  of  the  battery 
and  the  resistances,  and  a  steady  current  flows  through  the  galva- 
nometer as  indicated  by  the  arrow.  When  contact  is  made  with 
b}  a  varying  current  ic  will  flow  into  the  condenser  until  it  is 
fully  charged.  A  part  of  this  varying  current  flows  through  M 


FIG.  215. — Connections  for  Maxwell  method  for  determining  a  capacity 
in  absolute  measure. 

and  a  part  flows  upward  through  the  galvanometer,  tending  to 
deflect  it  in  a  direction  opposite  to  that  produced  by  the  steady 
current.  When  C  is  fully  charged,  the  currents  return  again  to 
their  steady  values.  By  properly  adjusting  the  arms  of  the 
bridge  and  the  number  of  times  per  second  the  condenser  is 
charged  and  discharged,  the  galvanometer  deflection  can  be 
reduced  to  zero,  which  means  that  the  net  quantity  displaced 
through  the  instrument  in  a  second  is  zero. 

When  e  and  b  are  not  in  contact,  the  currents  have  the  steady 
values  IM,  IN,  IP,  IG. 

Call  the  quantity  of  electricity  on  the  condenser  when  it 
is  fully  charged,  Qc.  Then 

Qc    =    C(P.D.)ad. 


366  ELECTRICAL  MEASUREMENTS 

As  the  currents  have  arrived  at  the  steady  state, 


IN       M  +  RG 
Consequently 

I0         =  IG  =  _N_ 

•    rpm         77?       TP      T  (jf    i  P(M  +  RG  +  N) 

.     .  \r.D.)ad  —  iQ^o  T  4>»     =  IG\K,Q    i     ~  — AT" — 


RG  +  AQ 
+  -       -  —     ^G 


and 


where  /G  is  the  galvanometer  current  when  the  circuit  is  in  the 
steady  state. 

When  e  touches  b,  a  varying  current,  ic,  which  finally  becomes 
zero,  flows  into  the  condenser  and  all  the  other  currents  are 
temporarily  altered. 

Let  the  alteration  in  IM  be  d!M 
in  IN  be  5IN 
in  IP  be  d!P 
in  IB  be  dIB 
in  IG  be  5IG 

If  QG  is  the  quantity  of  electricity  displaced  through  the  gal- 
vanometer by  the  current  dIG  at  each  contact  of  e  and  6  and  there 
are  n  such  contacts  per  second,  the  quantity  per  second  so  dis- 
placed will  be  nQG. 

Therefore,  if  the  galvanometer  stands  at  zero  under  the  com- 
bined action  of  IG  and  nQG, 

IG  +  nQG  =  0 
and 


,, 

To  find  QG,  the  quantity  displaced  through  the  galvanometer  by 
the  variable  current  8IG  when  the  condenser  is  charged,  suppose 
C  to  be  discharged  and  the  steady  currents  to  be  flowing  as  indi- 
cated in  Fig.  215.  The  potential  differences  between  the  ter- 
minals of  all  the  resistances  will  have  definite  values.  As  soon 


INDUCTANCE  AND  CAPACITY  367 

as  e  makes  contact  with  6,  the  varying  current  ic  flows  into 
the  condenser,  causing  temporary  alterations  in  the  currents 
through  M,  N,  RG,  B}  and  P.  The  change  in  P.D.  between  the 
terminals  of  any  one  of  the  resistances  is  the  change  in  the  cur- 
rent multiplied  by  the  resistance.  The  currents  d!B,  8IG,  etc., 
are  variable  and  become  zero  when  the  condenser  is  fully  charged. 
Referring  to  Fig.  215  it  will  be  seen  that 

81  M  =    ic  +  §IG 

81  B  =  81  M  +  81  N 

8IP  =  5IB  -      ic 

8IP   =  8IG  +  81  N 

81  N  ==  ol-B    —  ic  —  81  G. 

Using  the  changes  in  the  currents,  KirchhofTs  laws  may  be  applied 
to  the   meshes   M  RG  N  and  B  N  P  and  by  using  the  above 
relations  the  resulting  equations  may  be  expressed  in  terms  of 
the  resistances  and  the  variable  currents  dIB,  8IG  and  ic. 
For  the  mesh  M  RG  N  at  any  instant  during  charging, 


M(8IM)  +  R0(5I0)  +  _  N(dlN)  =  o 

or 

M(ic  +  dig)  +  Ro(dla)  +  L~^    ~  N(BIB  -  ic  ~  dIQ)    =  0. 

Uniting  terms  gives 
ic(M  +  N)  +  8IG(M  +  RG  +  N)  -  N(8IB)  +  ^f^  =  0.  (3) 

For  the  mesh  B  N  P  at  any  instant  during  charging, 
B(8IB)  +  N(8IB  -  ic  -  8IG)  +  P(8IB  -  ic)  =  0 
or  uniting  terms 

-  ic(  N  +  P)  -  8IG(N)  +  8IB(N  +  P  +  B)  =  0.  (4) 

Equations  (3)  and  (4)  may  be  integrated  to  obtain  the  total 
quantities  displaced  by  the  variable  currents  during  the  charging 
of  the  condenser;  8IG  is  zero  at  both  limits.  Therefore 

QC(M  +  N)  +  QG(M  +  RG  +  N)  -  QB(N)  -  0        (3a) 
and 

-  Qc(N  +  P)  -  QG(N)  +  QB(N  +  P  +  B)  =  0.  (4o) 


368         .        ELECTRICAL  MEASUREMENTS 
Eliminating  QB  gives 

M  +  Re+N-*   -r^~ 


Q< 


+  P  + 


Qa. 


(5) 


The  values  of  Qc  from  (2)  and  (5)  may  be  equated,  thus  eliminat- 
ing QG,  and  the  resulting  equation  solved  for  C. 


FIG.  216. — Commutator  used  by  Rosa  and  Dorsey  in  applying  Maxwell's 
method  for  the  absolute  measurement  of  electrostatic  capacity. 


C  = 


N 


nPM 


1  - 


N 


+PKM 


+ 


NB 


1  + 


NRa 


With  very  small  capacities  it  is  necessary  to  use  a  high  value  of 
n  (500  cycles  per  second),  and  high  voltages  (100  to  200  volts) 
in  order  to  obtain  sufficient  sensitiveness. 


INDUCTANCE  AND  CAPACITY  369 

The  capacity  as  determined  includes  that  of  the  commutator 
and  the  leads  to  the  condenser  under  measurement.  The  correc- 
tion due  to  these  capacities  is  determined  by  a  separate  measure- 
ment, the  leads  being  disconnected  from  the  condenser  without- 
altering  their  position  more  than  is  absolutely  necessary. 

The  commutator  used  by  Rosa  and  Dorsey  is  shown  in  Fig. 
216.  The  16  phosphor-bronze  contact  pieces,  Si,  S2,  etc.,  are 
carried  by  an  ebonite  disc  and  to  each  one  of  the  pieces  is  con- 
nected its  corresponding  section  of  the  brush  ring,  TI,  T2)  etc. 
This  ring  is  sectionalized  to  reduce  the  capacity  of  the  commutator 
and  to  allow  the  guard  ring  to  be  charged  and  discharged  syn- 
chronously with  the  main  condenser.  One  terminal  of  the  con- 
denser is  connected  to  the  copper  brush  B3.  The  brushes  BI 
and  B2  correspond  to  b  and  c  in  Fig.  215. 

The  condenser  is  charged  when  $3  touches  B\,  is  discharged 
when  it  touches  52,  and  so  on  for  each  contact  piece.  The  guard 
ring  is  charged  and  discharged  in  a  similar  manner  by  the  other 
side  of  the  commutator  (B6,  -B5,  54).  It  will  be  noted  that  the 
brushes  are  air-insulated  between  contacts,  thus  avoiding  the 
possibility  of  leakage  across  the  commutator  from  brush  to 
brush.  The  usual  speed  of  the  commutator  is  from  1,200  to 
1,500  revolutions  per  minute. 

Direct-deflection  Method  for  Comparing  Capacities. — The 
most  obvious  method  for  comparing  the  capacities  of  two  con- 
densers is  to  charge  the  condensers  from  the  same  battery  and  then 
to  determine  the  relative  quantities  which  they  have  accumulated 
by  discharging  them  in  turn  through  the  same  ballistic  galva- 
nometer. To  carry  out  this  test  in  its  simplest  form,  the  con- 
nections shown  in  Fig.  217  may  be  used. 


VWWWN/WV 

A  * 


/ 


FIG.  217. — Connections  for  direct  deflection  method  for  comparing 

capacities. 

24 


370  ELECTRICAL  MEASUREMENTS 

When  K  is  thrown  to  the  right-hand  stop  and  KI  is  depressed, 
the  condenser  Cx  is  charged  through  the  ballistic  galvanometer, 
giving  rise  to  a  deflection  6iX;  this  must  be  corrected  for  the 
multiplying  power  of  the  shunt,  mx.  A  similar  observation  with 
K  thrown  to  the  left  gives  0is,  the  multiplying  power  of  the  shunt 
now  being  ms.  If  the  damping  of  the  galvanometer  be  the  same 
in  the  two  cases, 

Cx  =  Q*  = 

Cs      Qs  ~ 
or 


If  the  damping  is  not  the  same  in  the  two  cases,  the  deflections 
must  be  corrected  (see  page  116).  Constant  damping  may  be 
attained  by  use  of  the  Ayrton  universal  shunt,  A. 

If  the  standard  and  the  unknown  are  of  very  different  capac- 
cities,  instead  of  shunting  the  galvanometer,  different  known 
voltages  may  be  used  in  the  two  tests,  and  an  allowance  made. 
This  procedure  is  convenient  if  an  Ayrton  shunt  is  not  at  hand. 

The  proper  value  of  the  standard  is  one  which  will  give  a  de- 
flection about  equal  to  that  due  to  the  unknown  capacity. 
Enough  battery  should  be  used  so  that  the  deflections  may  be 
read  with  good  precision. 

If  the  galvanometer  be  placed  at  a,  the  capacities  may  be  com- 
pared by  discharging  the  condensers. 

In  arranging  the  apparatus,  care  must  be  taken  that  the  capac- 
ities to  earth  of  long  leads  and  of  the  instruments,  as  well  as  the 
capacities  between  the  leads  to  the  condensers,  do  not  introduce 
errors.  For  instance,  the  leads  from  KI  to  the  condensers  should 
be  short,  of  small  wire  and  well  separated  from  the  leads  to  the 
other  side  of  the  condenser,  otherwise,  a  separate  test  must  be 
made  to  determine  their  capacity.  To  prevent  errors  from 
leakage,  the  battery  and  all  the  wiring  should  be  well  insulated, 
especially  the  keys  K  and  KI  and  the  leads  from  KI  to  the  con- 
densers via  K. 

Sources  of  Error.  —  In  reality  this  test  is  not  so  simple  as  might 
appear,  for  the  assumption  has  been  tacitly  made  that  the  eon- 
denser  is  entirely  charged  or  discharged  before  the  needle  of  the 
ballistic  galvanometer  has  moved  appreciably.  Reference  to  the 


INDUCTANCE  AND  CAPACITY 


371 


section  on  condensers  (page  357)  will  show  that  this  assumption 
is  strictly  true  only  for  air  condensers  charged  or  discharged 
through  a  negligible  resistance.  If  the  capacity  is  determined 
from  the  discharge  deflection,  both  the  first  rush  of  current  due 
to  the  free  charge,  and  the  gradually  decreasing  current  due  to 
the  liberation  of  the  absorbed  charge,  are  active  in  producing 
the  deflection,  and  the  galvanometer  needle  is  acted  on  by  two 
forces — a  sudden  blow  due  to  the  passage  of  the  free  charge  and 
a  long-continued  and  gradually  diminishing  push  due  to  the 
absorbed  charge.  Therefore,  when  there  is  considerable 'absorp- 
tion, the  apparent  capacity  as  determined  by  this  simple  method 


.25 


.05 


10    20    30    40    50    60     70     80    90   100  110  120 
Time  of  Charging  in  Seconds 

FIG.  218. — Showing  effect  of  time  of  charging  on  the  apparent  capacity  of 
sample  of  rubber-covered  wire. 

is  dependent  on  the  period  of  the  galvanometer  employed.  In 
working  with  the  discharge  deflection,  any  delay  after  the  con- 
denser is  disconnected  from  the  battery  and  before  it  is  con- 
nected to  the  galvanometer  will  cause  an  error  if  the  time  of 
charging  has  not  been  sufficiently  long  for  the  dielectric  to  be- 
come saturated,  for  absorption  goes  on  during  this  delay,  thus 
reducing  the  free  charge. 

In  industrial  testing  the  direct  deflection  method  is  very  com- 
monly applied  to  cables,  but  it  is*  obvious  that  to  obtain  results 
which  are  of  value  as  a  basis  of  comparison  between  samples 
which  are  nominally  the  same,  some  definite  procedure  must  be 
adopted. 

This  point  is  emphasized  by  Fig.  218,  which  shows  the  apparent 


372 


ELECTRICAL  MEASUREMENTS 


capacity,  on  discharge,  of  a  piece  of  rubber-covered  wire  when 
subjected  to  different  times  of  charging.  Specifications  for 
rubber-covered  wires  commonly  call  for  a  charging  period  of 
10  seconds. 

The  Zeleny  Discharge  Key. — In  order  to  obtain  the  free  charge 
capacity  of  a  condenser  with  an  imperfect  dielectric,  the  con- 
denser must  be  disconnected  from  the  galvanometer  after  it  has 
parted  with  its  free  charge  and  before  any  appreciable  portion 
of  the  absorbed  charge  has  been  given  up.  This  may  be  accom- 
plished by  the  Zeleny  discharge  key,8  shown  diagrammatically 
in  Fig.  219.  In  this  key  there  are  three  flexible  leaves,  LI,  L2,  and 
L3.  As  shown,  the  condenser  C  is  being  charged  from  the  bat- 
tery B.  When  the  key  is  depressed  the  battery  circuit  is  broken 


L3 


c          d 


FIG.  219. — Diagram  for  Zeleny  discharge  key. 

at  a,  and  the  discharge  circuit  completed  at  b.  On  continuing 
the  depression,  mechanical  contact  is  made  at  c,  and  the  dis- 
charge circuit  broken  at  d.  The  period  of  delay  before  the  gal- 
vanometer is  taken  out  of  circuit  is  controlled  by  varying  the 
distance  s,  by  turning  the  milled  head  e.  The  key  must  be  kept 
depressed  until  the  first  elongation  has  been  completed. 

In  using  this  key  one  starts  with  the  distance  s  large  (5  mm.) 
and,  maintaining  as  nearly  as  may  be  a  constant  velocity  oj 
tapping,  successive  throws  of  the  galvanometer  needle  are  ob- 
served as  s  is  diminished.  TJie  result  will  be  as  shown  in  Fig 
220.  The  deflections  fall  off  regularly  until  the  point  is  reachec 
where  sufficient  time  has  not  been  allowed  for  the  condenser  to 
part  with  its  free  charge.  After  this,  the  deflections  rapidly 
decrease  and  the  ordinary  variations  in  the  velocity  of  tapping 


INDUCTANCE  AND  CAPACITY 


373 


begin  to  cause  irregularities.     The  results  are  independent  of 
the  period  of  the  galvanometer. 


ace   S   in  Terms  of  Number  of  Turns,  of  Screw  & 


FIG.  220. — Illustrating  results  attained  by  use  of  Zeleny  discharge  key. 

Deflection  Method  Using  a  Commutator. — By  means  of  a 
rotary  commutator  the  condenser  may  be  rapidly  charged  and 
discharged,  possibly  100  times  a  second.  The  galvanometer  will 
then  take  up  a  steady  deflection,  and  after  the  instrument  has 
been  properly  calibrated  the  capacity  may  be  calculated.  This 
method  is  adapted  to  the  measurement  of  small  capacities  which 
are  without  absorption  and  leakage;  for  example,  air  condensers, 
or  the  capacities  between  wires  arranged  as  in  a  transmission 
line. 

The  commutator  by  which  the  charging  and  discharging  are 
effected  should  be  substantial  in  design  and  directly  driven  by  a 
motor  of  considerable  power  which  is  provided  with  a  flywheel 
and  supplied  with  current  at  a  fixed  voltage  so  that  the  number 
of  discharges  per  second  may  be  constant.  Fig.  221  shows  the 
device  as  used  by  Fleming  and  Clinton.10 

In  order  to  obtain  good  contacts  copper  brushes  should  be 
employed.  It  is  essential  that  surface  leakage  at  the  commu- 
tator be  eliminated.  For  this  reason  the  brushes  as  they  pass 
from  one  active  segment  to  the  next  must  not  be  supported  by 
substances  like  mica  or  agate,  for  after  a  time  these  become  cov- 
ered with  a  conducting  coating.  Air  must  be  used  as  the  insula- 
tion between  the  segments. 

In  the  form  of  commutator  shown  in  Fig.  221,  A  and  B  are  two 
rown  wheels  of  composition,  about  4  in.  in  diameter.  They  are 


374 


ELECTRICAL  MEASUREMENTS 


thoroughly  insulated  from  the  shaft  and  from  each  other  by 
bushings  and  washers  of  hard  rubber.  7  is  a  toothed  wheel  insu- 
lated from  A  and  B  and  from  the  shaft  and  serves  merely  as  a 
support  for  the  brush  as  it  passes  from  A  to  B,  thus  preventing 
mechanical  shock  and  undue  wear.  The  brushes  1  and  3  make 
contact  with  the  continuous  portions  of  A  and  B;  as  the  com- 
mutator revolves  2  is  alternately  connected  to  A  and  to  B  and 
the  condenser  is  rapidly  charged  and  discharged.  At  their 


FIG.  221. — Fleming  and  Clinton  commutator  for  use  in  comparing  capacities. 

peripheries  the  wheels  A,  B,  and  I  are  separated  by  air  spaces. 
Means  for  accurately  determining  the  speed  must  be  provided. 

If  the  condenser  has  a  capacity  of  C  microfarads  and  is  dis- 
charged through  the  galvanometer  n  times  per  second,  the  vol- 
tage of  the  battery  being  V,  the  quantity  displaced  through  the 
galvanometer  in  1  sec.,  or  the  average  current,  will  be 

nCV 

~W 

K  is  the  constant  of  the  galvanometer  and  DI  the  deflection.  To 
determine  K  a  steady  current  from  the  same  battery  may  be 
sent  through  the  instrument  and  regulated  by  the  insertion  of  a 


INDUCTANCE  AND  CAPACITY  375 

series  resistance,  R,  and  a  shunt,  S,  on  the  galvanometer.     Call 
the  deflection  so  obtained  D2;  then 

S106 


The  two  deflections  should  be  approximately  equal. 

A  better  procedure  was  adopted  by  Fleming  and  Clinton,  who 
used  a  special  differential  galvanometer  of  the  D'Arsonval  type. 
The  two  movable  coils  were  rigidly  attached  to  the  same  vertical 
insulating  stem,  one  above  the  other,  each  coil  having  its  own 
permanent  magnet.  The  adjustment  for  obtaining  an  exactly 
differential  instrument  was  by  means  of  a  magnetic  shunt.  This 
construction  allows  the  two  coils  to  be  highly  insulated,  which  is 
essential  in  order  that  the  results  may  not  be  vitiated  by  cross- 
leakages,  since  the  voltage  employed  on  the  condensers  may  be 
considerable  —  100  volts  or  more.  One  coil  is  traversed  by  the 
discharges  from  the  condenser,  while  the  other  carries  a  steady 
current  derived  from  the  battery.  When  the  instrument  stands 
at  zero, 

=  n[(R0 

A  separate  experiment  must  be  made  to  determine  the  capacity 
of  the  leads. 

Thomson  Method  for  Comparing  Capacities.11—  If  two  con- 
densers be  charged  with  equal  quantities  of  electricity  the 
voltages  required  will  be  inversely  as  the  capacities.  To  take 
advantage  of  this  relation  some  ready  means  must  be  provided 
for  indicating  when  the  charges  are  equal  and  for  showing  the 
relative  voltages  applied  to  the  condensers.  The  arrangement 
shown  in  Fig.  222  is  that  necessary  for  carrying  out  the  measure- 
ments according  to  Thomson's  method.  The  battery  current 
flows  through  Ri  and  #2  in  series.  If  KI  and  K2  are  both  de- 
pressed at  the  same  time,  Cx  is  charged  to  a  voltage  IR  i  while 
CP  is  charged  to  a  voltage  IR2.  When  KI  and  K2  are  released 
and  make  contact  with  their  back  stops,  the  condensers  are  con- 
nected in  series  +  to  —  so  that  their  charges  tend  to  neutralize 
each  other  or  "mix."  To  see  if  the  neutralization  is  perfect, 
that  is,  to  see  if  there  were  equal  quantities  on  the  two  condensers, 


376 


ELECTRICAL  MEASUREMENTS 


Ks  is  depressed  and  the  unneutralized  portion  of  the  charge  sent 
through  the  galvanometer,  the  deflection  of  which  will  be  to  the 
right  or  to  the  left  according  to  which  charge  preponderates.  By 

r> 

successive  trials,  altering  ~'  the  galvanometer  deflection  may  be 

/I2 

reduced  to  zero.     Then 


To  carry  out  the  test  a  special  key  which  combines  K\,  K%  and  K$ 
on  a  single  base  is  usually  employed..    In  manipulating  this  key 


FIG.  222. — Connection  for  Thomson  method  of  comparing  capacities. 

care  must  be  taken  that  it  performs  its  functions  properly  and 
that  cross-contacts  by  the  fingers  of  the  observer  are  avoided. 

To  obtain  a  good  precision  the  variable  resistances  Ri  and  Rz 
should  be  high  so  that  their  adjustment  may  be  sufficiently  flexible. 
If  resistance  boxes  are  used  the  smallest  step  is  usually  1  ohm,  so 
when  comparing  ordinary  condensers  the  resistance  which  is  ad- 
justed should  be  at  least  1,000  ohms.  In  submarine  cable  work 
much  higher  resistances  are  employed;  Ri  +  R2  may  be  as  much 
as  100,000  ohms.  The  galvanometer  must  be  very  sensitive  and 
the  battery  voltage  as  high  as  is  consistent  with  safety  of  the 
apparatus.  With  high  voltages,  to  avoid  throwing  an  unduly 
large  potential  on  either  condenser,  the  known  and  unknown 
capacities  should  be  about  the  same. 

When  cables  are  tested,  the  core  is  connected  to  a,  and  b  then 
becomes  the  common  " ground";  in  this  case  perfect  insulation 
of  the  battery  is  essential. 


INDUCTANCE  AND  CAPACITY  377 

The  resistances  R i  and  R2  and  their  leads  must  be  thoroughly 
insulated. 

The  effect  of  any  considerable  leakage  in  Cx  during  the  period 
of  charging,  is  practically  to  shunt  Ri  by  the  leakage  resistance, 
so,  to  get  equal  quantities  on  the  condensers,  Ri  as  unplugged  in 
the  resistance  box  must  be  made  larger  than  if  the  condenser 
had  been  of  the  same  capacity  and  devoid  of  leakage.  Thus  the 
apparent  capacity  will  be  too  small. 

In  this  case,  the  procedure  recommended  is  to  use  instead  of 
the  resistance  unplugged  in  the  box,  the  parallel  resistance  of  RI 
and  the  condenser  under  test.  This  necessitates  a  measurement 
of  the  insulation  resistance  of  the  condenser.  The  period  be- 
tween charging  and  mixing  must  be  made  as  short  as  possible, 
since  leakage  during  this  time  will  cause  the  charge  on  the  un- 
known to  be  too  small,  which  will  necessitate  an  increase  in  Ri 
above  the  proper  value.  Leakage  during  mixing  will  reduce,  by 
shunting,  the  quantity  to  be  discharged  through  the  galvanometer 
and  will  thus  diminish  the  sensitiveness  of  the  method. 

If  absorption  be  present,  it  is  necessary  to  adopt  some  definite 
cycle  of  operations  in  order  to  obtain  comparable  results,  for  the 
behavior  of  an  imperfect  condenser  depends  to  a  certain  extent 
on  its  previous  history,  that  is,  on  the  voltage  to  which  it  has  been 
subjected,  the  time  of  electrification  and  the  duration  of  the  charg- 
ing and  mixing  periods,  together  with  the  completeness  of  the 
discharge. 

As  the  absorbed  charges  reappear  gradually  and  as  it  is  the 
free  charges  which  are  to  be  neutralized,  the  key  Kz  must  be  closed 
for  only  an  instant,  when  observing  the  galvanometer.  The 
condensers  should  be  completely  discharged  between  the 
observations. 

Gott  Method  for  Comparing  Capacities.12 — The  connections 
for  Gott's  method  are  shown  in  Fig.  223.  If  condensers  are  being 
compared,  acbd  including  the  galvanometer  circuit  is  a  perfectly 
insulated  system.  "The  condensers  being  discharged,  the  key  KI 
is  depressed,  thus  sending  a  current  through  the  circuit  cad  and 
charging  the  condensers  Cx  and  CP  in  series.  Then 

Vda    _    RN 
Vac    ==    RM 


378 


and 


ELECTRICAL  MEASUREMENTS 


Cx  = 


If  KZ  be  depressed,  still  keeping  KI  closed,  there  will,  in  general, 
be  a  deflection  of  the  galvanometer,  due  to  the  difference  in  the 
potentials  of  a  and  b.  If  there  is  a  deflection,  K\  and  Kz  are 
raised  and  the  condensers  completely  discharged  by  the  use  of  K%. 

7-> 

After  this  another  test  is  made  with  a  different  value  of  -^-' 

KM 

By  successive  trials,  adjusting  either  RM  or  RN,  the  deflection  due 
to  the  difference  of  potential  of  a  and  6  at  the  instant  of  closing 
K2  may  be  reduced  to  zero.  When  the  adjustment  is  complete, 


=  CP 


R 


M 


d 
FIG.  223. — Connections  for  Gott  method  for  comparing  capacities. 

As  anything  which  gives  rise  to  a  false  distribution  of  potentials 
in  the  network  acbd  will  cause  errors,  all  parts  must  be  carefully 
insulated,  and  K2  especially,  as  it  is  handled.  Leakage  within 
the  battery  or  between  the  battery  leads  is  not  a  source  of  error, 
as  it  merely  alters  the  P.D.  applied  to  the  network.  Direct 
leakage  from  the  battery  to  the  condenser  circuits  must  be 
avoided.  Any  leakage  between  the  terminals  of  either  condenser 
is  a  source  of  error;  this  leakage  may  be  through  the  dielectric 
of  the  condenser  or  between  the  leads.  If  Cx  be  imperfect  in 
this  respect  and  K \  be  kept  depressed,  the  potential  of  b  gradually 
approaches  that  of  c.  The  value  found  for  Cx  will  then  be  too 
great  and  will  increase  with  the  time  of  charging. 

When  cables  are  measured  the  core  should  be  connected  to 


INDUCTANCE  AND  CAPACITY  379 

6,  as  the  sheath  is  necessarily  grounded.  Because,  of  the  small 
effect  of  battery  leakage,  this  method  is  very  commonly  employed 
in  submarine  cable  work. 

If  the  rates  of  absorption  of  the  two  condensers  are  not  the  same, 
the  results  obtained  will  be  dependent  on  the  time  of  charging. 
For  condensers,  and  for  cables  up  to  a  length  of  about  1,000 
knots,  a  correction  devised  by  Muirhead  and  intended  to  correct 
for  both  absorption  and  leakage  is  applicable;  it  fails,  however, 
in  the  case  of  cables  of  greater  length,  supposedly  on  account 
of  the  retardation  due  to  the  resistance  of  the  cable  itself.12 

The  methods  of  Thomson  and  of  Gott  are  of  importance  in  sub- 
marine cable  testing.  In  this  work,  exceedingly  large  capacities 
must  be  measured,  frequently  several  hundred  microfarads.  It 
is  in  connection  with  these  measurements  that  the  complications 
due  to  leakage  and  absorption  become  most  troublesome. 

Elementary  Methods  of  Determining  Inductance  and  Capacity 
by  Alternating  Currents.13  —  If  a  sinusoidal  current  of  known 
frequency  be  used,  the  most  obvious  method  of  measuring  an 
inductance  is  to  determine  the  current  and  the  P.D.  between  the 
terminals  of  the  coil.  Then  if  o>  is  2ir  times  the  frequency,  R 
the  resistance,  V  the  applied  voltage  and  I  the  current,  the  in- 
ductance is  given  by 


or  if  the  resistance  is  negligible,  by 

l-a- 

When  the  current  wave  is  non-sinusoidal  it  is  possible  to  allow 
for  the  effect  of  the  harmonics.  Suppose  that  the  maximum 
values  of  the  various  components  are  I\,  Iz,  /5,  etc.  Then 

i  =  Ii  sin  ut  +  73  sin  (3co£  —  03)  +  75  sin 
The  effective  value  of  the  current  will  be 


'  =  V¥+¥+¥+-- 

The  fundamental  equation  for  the  flow  of  current  through  an 
inductive  resistance  is 

v  =  Hi  +  L~- 


380  ELECTRICAL  MEASUREMENTS 

From  the  above, 


v  =  R[Ii  sin  wt  +  /3  sin  (3co£  -  03)  +  /5  sin  (5co£  -  05)  +  .    -    . 
i  cos  co£  +  3/3  cos  (3orf  -  03)  +  5/5  sin  (5coZ  -  05)  +  .    .    . 


The  mean  square  value  of  the  P.D.  will  be 

F2  =  /2fl2  +  co2/,2  [^  +  9  ~-  +  25  ^ 
therefore, 

L  = 


/    /!2  +  /32 

\/12+9/32 


!+25/52+  .  .  . 
When  the  resistance  is  negligible, 


(7) 


In  this  case,  suppose  the  P.D.  wave  has  been  analyzed.     Then  at 
any  instant, 

v  =  Vi  sin  co£  +  F3  sin  (3co^  -  09)  +'  F5  sin  (5co^  -  05)  +  .    .    . 
Therefore 

—  Li  =  —  cos  co£  +  T  —  cos  (3co^  —  63)  +  -.p—  cos  (5coi  —  06)  +  • .  . 

CO  OCO  OCO 

The  mean  square  value  of  Li  will  be 


and 


!/2       co2  '     2    +  9co2  '     2    +  25co2       2    +  '  ' 

F     /TV — i  F32 — i — rv^ 

L  =    TcoT  V  "2~  +  9  "2~  +  25  '  ^2"  +  '  ' 


or 

T       V     /F12  +  ^F32  +  K5TV+  .77 

=  Ico  V~      VS  +  F^+lV^T 

Capacity  Measurements. — The  current  through  a  condenser 
with  a  perfect  dielectric  is  given  by 

i  -  C  -- 
1  "  °  dt 


INDUCTANCE  AND  CAPACITY  381 

Assuming  sinusoidal  currents  the  capacity  is 

C-  ±- 

~  wy 

If  the  applied  e.m.f.  is  not  sinusoidal,  the  harmonics  will  be 
exaggerated  in  the  current  wave,  for  the  current  is 


-  03)  +  575cos(5co£  -  05) 
Using  root-mean-square  values, 


Therefore, 

C 


BRIDGE  MEASUREMENTS   OF  CAPACITY  AND  INDUCTANCE 

As  originally  devised,  many  of  the  methods  for  comparing 
capacities  and  for  comparing  inductances,  as  well  as  methods 
for  determining  an  inductance  in  terms  of  a  capacity,  depended 
on  the  employment  of  variable  currents.  As  the  industrial 
uses  of  alternating  currents  have  developed,  especially  in  connec- 
tion with  telephony,  it  has  become  important  that  tests  be 
made  under  conditions  which  are  as  nearly  as  possible  those 
pertaining  to  the  ordinary  use  of  the  apparatus.  Hence, 
alternating  currents  have  replaced  the  variable  currents  formerly 
employed  and  the  methods  for  capacity  measurement  have  been 
so  modified  that  they  give  data  of  value,  in  addition  to  determining 
the  capacity  of  the  condenser  under  measurement. 

Condition  for  Zero  Indication  of  Detector. — When  variable 
currents  are  used  in  balance  methods  for  measuring  inductance 
and  capacity,  a  long  period  galvanometer  is  employed  as  the 
detector.  The  arrangement  of  the  circuits  is  such  that  at  balance 
no  permanent  current  flows  through  the  instrument ;  this  being 
so — 

1.  The  deflection  will  certainly  be   zero   if  no   current  flows 
through  the  galvanometer  at  any  time  during  the  establishment 
of  the  permanent  state  of  the  circuit. 

2.  Presumably  the  deflection  will  also  be  zero  when  the  net 


382  ELECTRICAL  MEASUREMENTS 

quantity  of  electricity  displaced  through  the  instrument  during 
the  establishment  of  the  permanent  state  of  the  circuit  is  zero, 
or  when 

I  iadt  =  QG  =  0. 
Jo 

If  i0  =  0  continuously,  then  necessarily  QG  =  0.  The  converse 
is  not  true,  for  the  net  quantity  may  be  made  zero  by  a  current 
which  flows  through  the  detector  first  in  one  direction  and  then 
in  the  reverse  direction.  When  deducing  the  conditions  which 
must  be  fulfilled  in  order  that  the  galvanometer  may  remain 
undeflected,  it  is  best  to  impose  the  condition  that  no  current 
shall  flow  through  the  galvanometer  at  any  time,  for  in  some 
cases  the  galvanometer  needle  will  be  disturbed  even  though  the 
integral  current  is  zero.27  The  disturbance  depends  on  the 
alteration  of  the  strength  of  the  galvanometer  needle  by  the 
transient  current.  In  a  general  way,  the  reason  for  the  deflec- 
tion may  be  seen  by  supposing  the  instrument  to  be  traversed 
by  an  alternating  current.  If  the  magnetism  of  the  needle  is 
affected  by  the  current,  the  galvanometer  becomes  in  effect  a 
soft-iron  instrument  with  a  magnetic  control  and  there  will  be 
a  deflecting  moment  proportional  to  the  square  of  the  current. 
In  the  case  of  the  steadily  applied  alternating  current  the  needle 
will  come  to  rest  in  a  deflected  position  depending  upon  the 
strength  of  the  current. 

Some  moving-coil  instruments  are  subject  to  this  same  error, 
when  used  as  detectors  for  integral  currents. 

As  an  example  of  a  method  where  the  phenomenon  is  of  im- 
portance, take  the  comparison  of  two  mutual  inductances  by  the 
method  given  on  page  416.  The  integral  flow  of  current  through 
the  galvanometer  will  be  zero  if 

mx      TX 
mP       rP 

That  the  current  through  the  galvanometer  may  be  zero  con- 
tinuously it  is  necessary  that 


~  (A) 

Tp 


and 

«£ 
mP 


INDUCTANCE  AND  CAPACITY 


383 


On  trying  the  experiment  it  will  be  found  that  unless  the  rela- 
tion (B)  is  approximately  fulfilled  the  needle  will  be  slightly 
disturbed. 

In  the  following  proofs,  except  in  those  for  De  Sauty's  method 
for  comparing  capacities  where  the  application  of  both  condi- 
tions for  balance  will  be  illustrated,  the  condition  iG  =  0  con- 
tinuously will  be  imposed. 

De  Sauty  Method  for  Comparing  Capacities. — This  method  is 
adapted  to  the  comparison  of  condensers  without  leakage,  which 
are  either  free  from  absorption  or  have  equal  rates  of  absorption. 
Fig.  224  shows  the  connections. 


FIG.  224. — Connections  for  De  Sauty  method  for  comparing  capacities. 

The  two  bridge  arms  RM  and  RN  are  non-inductive  resistances. 
Cx  and  CP  are  the  two  condensers  which  are  to  be  compared. 
The  detector,  which  will  be  considered  as  having  both  inductance 
and  resistance,  is  at  G. 

When  the  key  K  is  against  the  back  stop  the  condensers  are 
discharged.  The  arms  RM  and  RN  are  adjusted  until  on  depress- 
ing K  the  detector  gives  no  indication.  Then 


^x  —  ^p  Ti — 
KM 

To  prove  this  relation,  condition  1  (page  381),  will  first  be  applied. 
In  that  case,  the  variable  current  iM  is  that  flowing  into  cohdenser 
Cx  and  the  variable  current  iN  is  that  flowing  into  CP,  and  at 
every  instant 

l  M  _   RN, 

IN       RM 


384  ELECTRICAL  MEASUREMENTS 

The  potential  difference  between  6  and  c  is 

Vbc  =  ^r-  \iMdt 
and  between  d  and  c  it  is 


-,  „  j_  f -^ 


F&C  must  equal  F^c  since  at  no  time  during  the  establishment  of 
the  steady  state  does  any  current  flow  through  G.     Then 


i  r  ,,     i  r.  ,    Ra  i  r. 

-FT  I  iMat  =  -7r  \  INUI  =  j-,     -~r  I  i 

L/X   JO  ^Pj  tiN       LpjQ 


RN 

RM 


FIG.  225. — Mesh  diagram  for  De*  Sauty  method  for  comparing  capacities 


If  the  condition 


r 

ition   I  iGdt  = 
Jo 


QG  =  0  be  applied,  the  demonstration 


is  more  complicated,  since  the  expression  for  QG  must  first  be 
deduced  and  then  the  condition  found  which  renders  it  zero. 
Consider  that  the  bridge  is  arranged  as  in  Fig.  225. 

Assume  that  during  the  time  of  charging  the  condensers,  that 
is,  until  the  steady  state  has  been  established,  the  meshes  are 
traversed  by  the  variable  currents  x,  x  +  y,  and  iB,  which 
finally  become  zero. 

Taking  the  mesh  abd, 


x(RM  +Ra+ 


La       -  (x  +  y)  R0  -  L 


-  iaRN  =  0 


INDUCTANCE  AND  CAPACITY  385 

or  uniting  terms, 

X(RM  +  RN}   ~  yRo  ~  LG  ^  -  iBRN  =  0.  (10) 

Considering  the  mesh  bed,  the  potential  difference  between  b  and 
c  is 


Vbc  =  7r~  I  (x  +  y)dt,    and  similarly  for 
Hence 


r-  \( 

'X   JO 


dx       d\  dx 

L°        =° 


or  uniting  terms, 

i     (*t  1    f*t  si 

-FT  \(x  +  y)dt  +  c   I  (x  +  y  -  iB)dt  +  yRG  +  LG  ^  =  0.  (11) 
^xjo  ^pjo  ds 

(10)  and  (11)  may  be  integrated  from  t  =  0,  when  the  key  K  is 
closed,  to  the  time  t  when  the  permanent  state  has  been  estab- 
lished. Call  Qx  the  quantity  displaced  by  the  current  x  in  that 
time,  QG  the  quantity  displaced  through  the  galvanometer  by  y,  the 
true  galvanometer  current,  and  QB  the  quantity  displaced  by  iB. 
Integrating  (10)  and  remembering  that  y  is  zero  at  the  start  and 
zero  at  the  finish, 

Qx  (RM  +  RN)   ~  QoRo  ~  QnRN  =  0.  (lOd) 

Integrating  (11)  gives 

(Qx  +  QG)  4-  +  (Qx  +  QG-  QB)  )r  =  0.  (lla) 

L>x  ^P 

From  (lOa)  and  (lla), 


(12) 


n      QoRo  +  QsRN          f\      f\   t     Cx 

Qx         pip 

KM    i    KN 

VtfG'  ~T  *tB    \  si         \      n 
\(^X  ~T   ^P 

Q*\(Rx+R 

\               x                  p 

N'  C    -4-  C      ~ 

'  n 

^  X      1      *^  P                        —  * 

"Q°~                     RM~ 

h  #G  +  ^ 

If  QG  =  0, 

Cx 

^,v 

Cx  +  CP        RM  + 
25 


386 
or 


ELECTRICAL  MEASUREMENTS 


R 


as  before. 


(13) 


Maxwell  Method  for  Comparing  Inductances. — An  induct- 
ance may  be  compared  with  a  variable  standard  by  an  analogous 
method  due  to  Maxwell.* 

The  arrangement  of  the  circuits  is  shown  in  Fig.  226.  As 
before,  RM  and  RN  are  adjustable  non-inductive  resistances. 
Lx  and  LP  are  the  inductances  to  be  compared;  they  have  resist- 
ances Rx  and  RP  respectively.  In  order  to  make  the  adjust- 
ment expeditiously,  it  is  necessary  to  include  a  variable  non- 

6 


FIG.  226.  —  Mesh  'diagram  for  Maxwell  method  for  comparing  inductances. 

inductive  resistance,  R,  which  can  be  thrown  into  the  arm 
Lx  if  necessary,  by  changing  the  battery  lead  from  c  to  e  and  to 
use  for  LP  a  variable  standard  of  inductance  having  a  constant 
resistance. 

The  adjustment  is  made  in  two  steps;  a  probable  value  of  the 

T> 

ratio  -TSJ-  is  chosen,  and  keeping  KI  closed,  the  resistance  R  is 


adjusted  until  balance  is  obtained.  In  this  case  the  arrange- 
ment is  an  ordinary  Wheatstone  bridge,  only  the  resistances 
coming  into  play.  When  the  adjustment  is  complete, 

RM  Rx 


D  '     D      _1_    D 

£1N          tip  -\-  K 

After  the  balance  has  been  effected,  KI  is  released  and  K^  kept 
closed.  LP  is  now  varied  until  the  detector  gives  no  indication 
when  contact  is  made  and  broken  at  K\.  Then 


Treatise  on  Electricity  and  Magnetism,"  third  edition,  Art.  757. 


INDUCTANCE  AND  CAPACITY  387 

Lx=I*f*-  (15) 

K>N 
n 

Several  trials  with  various  values  of  ^~  may  be  necessary  before 

KN 

the  proper  ratio  is  found. 

In  this  and  other  methods  where  the  balance  is  independent 
of  the  frequency,  a  " buzzer"  operating  through  a  telephone  in- 
duction coil  is  often  a  convenient  source  of  supply  for  the  inter- 
rupted current,  the  detector  being  a  telephone. 

To  prove  the  relation  (15)  the  first  condition  stated  on  page 
381  may  be  imposed.  After  the  adjustment  is  complete  no 
current  passes  through  the  detector  at  any  time,  so  for  all  values 
oH, 

Vbc  =  Vdc 
V  i.  —  V  j 

'   ab  '   ad 


IN         KM         IP 
Therefore 


dix       v  (p    _j_  v\       T     dip 
-jr  =  IP(KP  +  H)  +  LP  -~rr 


so 


which  must  be  true  for  all  values  of  t. 


and 


Rx  —  D"  (R 
KN 


In  order  to  balance,  the  bridge  when  all  four  of  the  arms  are 
inductive,  three  instead  of  two  conditions  must  be  satisfied,  as 
will  be  seen  from  the  following. 


388 


ELECTRICAL  MEASUREMENTS 


Suppose  that  no  current  flows  through  the  detector  at  any 
time.     Then  referring  to  Fig.  227 

V«b   =    Vad 

vbc  =  vdc 

ix  =  IM 

ip    —  ^B  —  ix  =  is  —  IM 
IN  =  IB  —  iu> 


FIG.  227. — Mesh  diagram  for  Maxwell  bridge  with  four  inductive  arms. 
Therefore,  making  no  assumption  as  to  the  relation  of  iB  to  t, 


(RM  H~  RN^M  +   (Lii  +  LN)  — v-    —  RN^B  4~  LN 


diB 
dt 


(16) 


and 


(R 


(L,+L,)^f  = 


L-¥-    ^17) 


Eliminating  iM  between  (16)  and  (17)  gives 

diM 
dt 

—r  [  —  RpLN  -\-  RNLP  —  RxLN  -\-  RMLP]  +  iB[R 


(RM  +  RN)(LX 


-  (Rz  +  RP)(LM 


(18) 


Eliminating  -       between  (16)  and  (17)  gives 


diB 
dt 


[LffLx  —  Z/3/Z/p]  -|-  IB  [  —  RpLff  -f-  RffLp 


(RM  +  RN)(LX 


-  (Rx 


LN) 


(19) 


INDUCTANCE  AND  CAPACITY  389 

The  value  of     !*   derived  from  (19)  when  equated  to  that  in 
(18)  gives 


[LNLX  — 


iB[RNRx  -  RMRP]  =  0.  (20) 

By  supposition  (20)  must  hold  for  all  values  of  t  and,  therefore, 
for  the  steady  state,  so 

RNRX  -  RMRP  =  0  (21) 

which  is  the  ordinary  condition  for  the  balance  of  the  Wheatstone 
bridge.     In  order  that  (20)  may  be  true  for  all  values  of  t  the 

coefficients  of  —~  and  -~  must  also  be  zero,  so 
at2  at 

LNLX  -  LMLP  =  0  (22) 

—  RpL/M  +  RN^X  +  RxLiN  —  RuiLp  —  0.  (23) 


As  no  assumption  has  been  made  concerning  the  relation  of 
IB  to  t,  equation  (20)  holds  when  the  bridge  is  supplied  with 
sinusoidal  as  well  as  with  variable  currents. 

The  Secohmmeter.14—  To  increase  the  sensitiveness  of  the 
bridge  methods  for  the  measurement  of  self-inductance  and 
capacity  which  depend  upon  the  use  of  variable  currents,  Ayrton 
and  Perry  devised  the  secohmmeter,  by  which  the  impulses  on  the 
galvanometer  needle  can  be  made  to  follow  one  another  so 
rapidly  that  the  instrument  takes  up  a  steady  deflection.  The 
arrangement  is  essentially  a  double  commutator.  One  of  the 
commutators  reverses  the  battery  connections  while  the  other 
reverses  the  galvanometer  terminals  so  that  the  impulses  on  the 
needle  of  the  instrument  are  always  in  the  same  direction. 
Referring  to  Fig.  228  the  shaded  portions  of  the  two  commutators 
are  made  of  an  insulating  material.  The  unshaded  portions  are 
conducting  segments.  The  brushes  aaf,  W,  and  cc',  ddf,  are  so 
placed  that  the  circuits  are  manipulated  in  the  proper  sequence. 
The  secohmmeter  is  driven  at  a  constant  speed  by  a  small 
motor. 

In  using  this  device  the  speed  must  not  be  so  high  that  suffi- 
cient time  is  not  allowed  for  the  establishment  of  the  steady 


390 


ELECTRICAL  MEASUREMENTS 


state  at  each  reversal.  Improved  forms  of  secohmmeter  have 
been  devised  by  Fleming  and  Clinton,  and  at  the  Bureau  of 
Standards. 

Battery 


Galvanometer 
,^-~ 
G 


FIG.  228. — Showing  connections  for  secohmmeter. 

The  Impedance  Bridge. — Because  of  the  nearer  approach  to 
actual  working  conditions,  capacity  and  inductance  measure- 
ments are  now  made  by  aid  of  alternating  currents,  preferably 

sinusoidal. 

Practically  all  the  recent 
researches  on  dielectrics  and 
condensers  as  well  as  the  pre- 
cision measurements  of  induc- 
tances have  been  made  by 
bridge  methods,  using  either 
the  impedance  bridge  or  the 
Anderson  bridge. 

In  the   impedance   bridge, 
FIG.  229.-Meshdiftgram  for  impedance  which  may  be  applied  to  the 

measurement  of  either  indue- 


b^ 


tance  or  capacity,  there  are  four  main  conductors  arranged  as 
in  the  Wheatstone  bridge.  Alternating  currents  are  employed 
and  either  two  or  four  of  the  conductors  are  reactive.  , 

To  deduce  the  condition  for  balance  the  arrangement  shown 
in  Fig.  229  may  be  taken. 


INDUCTANCE  AND  CAPACITY  391 

It  will  be  assumed  that  the  bridge  arms  have  impedances 
ZM,  ZN,  ZXj  ZP,  and  ZG  and  are  traversed  by  sinusoidal  cur- 
rents. All  the  impedances  are  expressed  in  symbolic  notation. 
The  mesh  currents  will  be  taken  as  indicated.  As  cognizance 
must  be  taken  of  their  phase  relations,  these  currents  must 
also  be  expressed  symbolically  and  referred  to  the  same  axis, 
for  instance,  IB-  Applying  KirchhofFs  laws,  for  the  X  mesh, 

X  (ZM  +  ZG  +  ZN)  -  (X  +  F)  ZG  -  IBZN  =  0, 
for  the  (X  +  Y)  mesh, 

(X  +  Y)(ZX  +  Zp  +  ZG)  -  XZ6  -  IBZP  =  0. 
Solving  for  Y,  the  current  through  the  detector, 
IB(ZPZM  —  ZNZx) 


v  = 


ZG(ZX  +  Zp  +  ZM  +  ZN)  +  (ZM  +  ZN)  (Zx 


If  the  detector  and  generator  be  interchanged,  the  value  of  the 
detector  current  becomes 

J^B^Z^ZX  ^_  ZP^ZM)  __  , 

' 


The  condition  for  no  current  in  the  detector  is 

ZNZX  =  ZPZM-  (26) 

Compare  the  above  with  corresponding  deduction  for  the  Wheat- 
stone  bridge,  page  183. 

The  generator  used  as  a  source  of  power  should  give  a  sinusoidal 
e.m.f.  wave. 

The  ratio  arms  (M  and  N)  may  be  non-inductive  resistances, 
highly  inductive  resistances,  or  perfect  condensers.  Bridges 
with  highly  inductive  ratio  arms  have  been  used  by  Giebe  in 
inductance  measurements20  and  by  Grover16  in  measurements 
of  the  capacity  and  power  factor  of  condensers. 

The  detector  may  be  either  a  telephone  or  a  .vibration  gal- 
vanometer. At  low  frequencies  the  latter  is  to  be  preferred,  for 
it  is  a  tuned  instrument  responding  freely  to  currents  of  only 
one  frequency.  With  it  an  accurate  balance  may  be  obtained 
even  though  the  currents  are  not  exactly  sinusoidal.  Electro- 
static disturbances  are  also  avoided. 

As  the  maximum  frequency  obtainable  with  the  vibration 


392  ELECTRICAL  MEASUREMENTS 

galvanometer  is  about  1,800  cycles  per  second,  a  limit  is  set 
above  which  the  telpehone  must  be  used.  The  sensitivity  of  a 
telephone  detector  may  be  greatly  increased  by  having  it  tuned 
to  the  frequency  of  the  supply,  especially  if  that  is  near  the  fre- 
quency at  which  the  ear  is  most  sensitive  (800  to  1,000  cycles 
per  second).  Of  course  with  any  tuned  detector,  the  periodicity 
of  the  current  must  be  kept  constant. 

Capacity  Measurements. — If  two  perfect  condensers  are  to 
be  compared,  they  may  be  placed  in  the  arms  P  and  X  (compare 
with  Fig.  225).  The  arms  M  and  N  may  be  non-inductive 
resistances.  In  this  case 

ZM  =  RM 


Substituting  in  (26)  gives 

7">  7"> 

/t\T  *tj 


r     -  r      ~ 

.  .         L/x   —   Up  D 
KM 

In  practice  the  comparison  of  ordinary  condensers  is  not  so 
simple,  for  an  energy  loss  may  occur  in  one  or  both  of  them.  As 
the  behavior  of  a  condenser  with  an  imperfect  dielectric  depends 
on  the  frequency,  it  is  important  thatxthe  correct  periodicity  be 
employed. 

If  energy  losses  be  present,  the  phase  of  the  current  in  RM 
will  probably  not  be  the  same  as  that  in  RN  and  no  adjustment 
of  these  resistances  can  be  found  which  will  cause  a  zero  indi- 
cation of  the  detector.  If  a  telephone  be  used,  there  will  be  a 
considerable  range  of  adjustment  over  which  the  sound  is  faint 
but  never  entirely  disappears. 

If  an  energy  loss  be  introduced  into  the  arm  of  the  bridge 
having  the  smaller  power  factor,  the  currents  in  RM  and  RN  may 
be  brought  into  phase  and  an  exact  balance  obtained.  Wien 
accomplishes  this  by  the  use  of  a  series  resistance  in  the  arm 
containing  the  better  condenser.15 


INDUCTANCE  AND  CAPACITY 


393 


The  bridge  is  arranged  as  shown  in  Fig.  230.  All  the  resist- 
ances are  supposed  to  be  non-inductive.  The  condensers  to 
be  compared  are  at  Cx  and  CP.  One  or  both  may  have  an  im- 
perfect dielectric,  and  to  duplicate  their  behaviors,  it  will  be 
assumed  that  perfect  condensers  having  effective  capacities  Cx 
and  CP  are  in  series  with  resistances  rx  and  rP  respectively. 
This  is  in  accordance  with  the  convention  mentioned  on  page  359. 
rx  and  rP  are  hypothetical  resistances  assumed  simply  as  an  aid 
in  the  demonstration  in  order  to  introduce  energy  losses,  their 
values  being  such  that  the  behavior  of  the  combination  of  the 
perfect  condenser  Cx  and  the  resistance  rx  will  be  the  same  as 
that  of  the  actual  condenser  at  Cx,  and  the  behavior  of  CP 
and  rP  the  same  as  that  of  the 
actual  condenser  at  CP.  The 
balance  arms  RM  and  RN  are 
variable  and  Rx  and  RP  are 
the  adjustable  resistances  used 
to  bring  the  potential  differ- 
ences Vcb  and  VCd  into  phase. 
Two  resistances  are  included 
because  it  may  not  be  known 
at  the  start  which  of  the  con- 
densers has  the  lower  power  . 
t  ^  i  £  ,1  FIG.  230. — Diagram  for  the  Wien  im- 

factor.     Only  one  of   the  re-  pedance  bridge. 

sistances  will  be  used. 

The  balancing  is  effected  as  follows:  with  Rx  and  RP  both 

73 

zero,  the  ratio  -—  is  adjusted  until  the  indication  of  the  detector 

is  a  minimum.     The  balance  is  then  improved  by  adjusting  Rx 
or  RP  as  the  case  may  require,  and  still  further  improved  by 

R 

readjusting  -—•  and  so  on,  thus  obtaining  a  perfect  balance  by 

successive  adjustments.     When  the  balance  is  effected, 

r     -  r    ^Nt 

^X  —  ^P   r> 

HM 

This  may  be  proved  as  follows;  in  general  by  (26) 

rz      rj  _     rj      ri? 

In  this  case 


394  ELECTRICAL  MEASUREMENTS 

. 

ZM  =  RM 
ZN  =  RN 

ZP  =   RP  -f-  TP  ---  ^7- 
coOp 

Zx  =  Rx  +  rP  --  i- 

coCA 

Substituting    in  (26)  gives 

' 

RM(BP.+  r>)  -  j          =  Rfl(Rx  +  rx)  -  j 


This  one  equation  being  in  complex  is  really  equivalent  to  two, 
for  when  all  the  terms  are  transposed  to  the  left-hand  side  the 
sum  of  all  the  horizontal  components,  "the  real  terms,"  must  be 
zero  and  the  sum  of  all  the  vertical  components,  "the  imaginary 
terms,"  must  also  be  zero.  Equating  the  vertical  components, 

RM          RN 

uCp  CoCy 

or 


Equating  the  horizontal  components, 

RM         Rx  +  rx 


(27) 
(21  a) 


RN        RP   +  TP 

Determination  of  Phase  Angle  of  Condenser.  —  As  previously 
denned,  the  phase  angle  of  a  condenser,  <p,  is  the  deviation 
of  the  phase  of  the  current  from  the  ideal  lead  angle  of  90°  which 
would  exist  in  a  perfect  condenser.  To  determine  the  difference 
of  the  phase  angles  of  Cx  and  CP,  (px  —  <PP,  from  (27)  and  (21  a), 

Rx  +  rx  =  RM  =  CP^ 
Rp  +  TP        RN         Cx 

When  multiplied   out  and  then  multiplied   through    by  co  this 
becomes 


but 

uCxrx  =  tan  <px    and    uCPrP  =  tan  $p 

tan  <px  —  tan  <pp  =  uCPRP  —  uCxRx.  (28) 


INDUCTANCE  AND  CAPACITY  395 

In  general,  tan  a  —  tan  b  =  (1  +  tan  a  tan  6)  (tan  (a  —  6)), 

so  if  the  phase  angle  <pP  of  the  standard  condenser  is  small,  as  it 
usually  will  be, 

tan  (<f>x  -  <pP)  =  uCpRp  -  uCxRx  (29) 

Either  Rx  or  RP  may  be  zero  as  previously  noted.  If  <pp  is  known, 
the  power  factor  of  the  unknown  condenser  is  readily  computed. 
The  values  of  <pP  and  CP  would  be  determined  by  a  process  of 
stepping  up  from  an  air  condenser.  The  curves  on  page  361 
were  determined  by  this  method.  As  it  is  customary  to  use  a 
high  frequency,  800  cycles  per  second  or  greater,  residual  in- 
ductances and  capacities  in  the  apparatus  must  be  reduced  to  a 
minimum.  The  sources  of  error  to  be  considered  when  refined 
measurements  are  to  be  made  are: 

1.  Inductance  or  capacity  of  M  and  N. 

2.  Error  in  the  ratio  of  M  and  N. 

3.  Inductance  or  capacity  of  Rx  and  RP. 

4.  Electrostatic    induction    between    the    bridge     and    its 
surroundings. 

Determination  of  Equivalent  Capacity  and  Conductance  of 
Condenser  or  Short  Length  of  Cable. — The  equivalent  capacity 
and  the  conductance  (leakance)  of  a  condenser,  or  a  short  length 
of  cable,  may  be  found  by  means  of  the  Wien  bridge.  A  short 
length  of  cable  is  specified  so  that  the  complications  arising  from 
distributed  capacity,  inductance,  resistance,  and  leakance  may 
be  avoided,  for  the  frequency  employed  is  likely  to  be  high. 

It  is  desired  to  find  the  combination  of  condenser  and  resistance 
in  parallel  with  it  which  will  duplicate  the  behavior  of  the  actual 
condenser.  No  assumption  is  made  as  to  the  nature  of  the  energy 
loss  taking  place  in  the  dielectric. 

The  arrangement  of  apparatus  is  that  shown  in  Fig.  230,  the 
specimen  being  connected  in  the  arm  X,  Rx  being  made  zero. 
CP  is  a  perfect  (air)  condenser,  in  series  with  a  non-inductive 
resistance,  RP,  and  both  are  adjustable.  To  balance  the  bridge 
it  is  necessary  to  bring  the  current  in  the  arms  N  and  P  into  phase 
with  that  in  the  arms  M  and  X.  This  may  be  done,  as  previously 
indicated,  by  putting  a  comparatively  small  resistance  in  series 
with  the  air  condenser,  or  by  shunting  that  condenser  with  a 


396  ELECTRICAL  MEASUREMENTS 

very  large  resistance;  usually  the  former  method  is  the  more 
convenient. 

In  general,  by  equation  (26) 

ZM%P  =  ZNZX. 
For  this  particular  case, 

Zi  M  ~  RM 
ZN  =  RN 


gx  - 


Substituting  these  relations, 


The  horizontal  component  gives 

W^  =  rpcjx  -    -£-• 
KM  UL'P 

The  vertical  component  gives 

bx  =  —  ~(fljT' 

Therefore,  the  two  components  of  the  admittance  of  the  condenser 
are 

gx  =  £(r- 

and 


~  ~*   '- 

\ 


The  power-factor  angle  0X  is  given  by 

1 


tan  Bx  =  —  =  — 
Qx 

The  conductance  gx  is  the  reciprocal  of  the  equivalent  insula- 
tion resistance  of  the  condenser  or  cable.     This  resistance  bears 


INDUCTANCE  AND  CAPACITY  397 

no  relation  to  the  dielectric  or  insulation  resistance  given  by 
measurements  with  steady  currents.  The  latter  may  be  many 
thousand  times  the  equivalent  dielectric  resistance  as  determined 
by  alternating  currents. 

Fleming  and  Dyke  in  their  researches  on  the  power  factor  and 
equivalent  conductivity  of  dielectrics18  used  a  bridge  in  which 
the  arms  M  and  N  were  formed  by  two  perfect  (air)  condensers. 
The  arm  P  contained  a  perfect  (air)  condenser  in  series  with  a 
non-inductive  resistance.  As  high  frequencies  were  used  (up 
to  6,000  cycles  per  second),  it  was  necessary  to  use  a  telephone 
detector. 

7          C1 

With  this  bridge  ~-  =  -^r~  ;  therefore,  referring  to  the  previous 
AN         \s  M 

demonstration, 


= 


CN  \1 


and 


CW  __  CP  __  \ 
"  CN\1  +rPzCPWr 


The  tangent  of  the  power-factor  angle  of  the  condenser  under 
investigation  is  given  by 

tan  e*  =  - 


When  air  condensers  are  used  in  the  bridge  arms  they  must  be 
properly  screened  or  else  placed  so  far  apart  and  so  far  from  the 
observer  that  difficulties  due  to  electrostatic  induction  are 
avoided.  All  the  connections  should  be  of  very  fine  wire. 

Bridge  for  Measurement  of  Electrolytic  Conductivity.  —  The 
impedance  bridge,  arranged  as  in  Fig.  231,  is  employed  in  the 
measurement  of  the  conductivities  of  electrolytes. 

On  account  of  the  capacity  action  in  the  electrolytic  cell  it  is 
necessary  to  use  an  adjustable  air  condenser  in  parallel  with  the 
resistance  in  the  arm  P.  When  the  bridge  is  balanced 


Wagner  Earth  Connection.  —  When  a  telephone  is  used  as  a 
detector  in  these  bridge  methods,  difficulties  are  encountered 
due  to  a  difference  of  potential  between  the  observer  and  the 


398 


ELECTRICAL  MEASUREMENTS 


telephone  he  is  using.  This  gives  rise  to  a  charging  current  in 
the  instrument  which  may  be  sufficient  to  prevent  an  exact 
balance  being  obtained.  The  trouble  may  be  eliminated  by 
bringing  the  telephone  and  the  observer  to  the  same  (earth) 


FIG.  231. — Diagram  of  bridge  for  determining  electrolytic  conductivities. 

potential  by  the  Wagner  Earth    Connection19  which  is  shown 

in  Fig.  232. 

The  adjustable  auxiliary  circuit  efg  is  similar  in  its  makeup 

to  the  bridge  circuit  adc.  It  is 
earthed  at  /  and  by  varying  its 
component  parts  the  impedances 
of  the  sections  ef  and  fg  can  be 
adjusted  and  the  potentials  of  e 
and  g  altered  in  reference  to  the 
earth. 

With  the  switch  s  open  the 
bridge  is  balanced  as  well  as  pos- 
sible, using  the  telephone  7Y 
Then  s  is  closed  and  the  impe- 
dance of  the  auxiliary  circuit 
adjusted  until  the  sound  in  Tz  is 

,   a  minimum.     This  means  that 
FIG.  232. — Diagram  for  Wagner  earth 

connection.  d  and  consequently  T\  are  con- 

tinuously at  practically  the  same 

potential  as  /,  which  is  earthed.  Therefore,  there  can  be  no  in- 
ductive action  between  the  telephone  "T\  and  the  observer.  After 
this  adjustment  has  been  made,  s  is  opened  and  the  final  balance 
is  obtained  by  adjusting  the  bridge  proper. 


INDUCTANCE  AND  CAPACITY 


399 


Inductance  Measurements. — In  the  comparison  of  an  induct- 
ance with  a  variable  standard  inductance  the  connections  shown 
in  Fig.  233  may  be  used. 

The  ratio  arms  RM  and  RN  are  non-inductive  resistances. 
The  variable  standard  of  self-inductance  is  at  P  (see  page  386). 
Lx  is  the  unknown  inductance  and  R  is  an  adjustable  non- 
inductive  resistance  which,  if  necessary,  may  be  placed  in  series 
with  the  unknown  inductance  by  changing  the  lead  from  c  to 
e.  A  and  D  are  sources  -of  alternating  and  direct  current, 
respectively;  T  and  G  are  the  corresponding  detectors  (compare 
Fig.  226). 


FIG.  233. — Diagram  of  impedance  bridge  for  comparing  inductances. 
The  impedances  of  the  bridge  arms  are 

ZM  =  RM 
ZN  =  RN 

Zp  =  tip  -f-  jit)Lp 
Zx  =  Rx  +  juLx. 

Substituting  these  values  in  the  general  equation  (26)  and 
separating  the  quadrature  components,  the  two  conditions  which 
must  be  fulfilled  in  order  that  the  bridge  may  be  balanced 
follow : 

From  the^horizontal  component, 


From  the  vertical  component, 


It, 


(30) 


(31) 


400  ELECTRICAL  MEASUREMENTS 

Therefore,  when  measuring  an  inductive  coil  a  perfect  balance 
implies  two  things — that  the  ohmic  resistances  are  balanced 
as  in  the  ordinary  Wheatstone  bridge,  and  that  the  inductances 
are  in  the  ratio  of  the  corresponding  bridge  arms.  If  there  are 
other  than  i2r  losses  in  the  arm  X  they  appear  in  Rx  which  in 
this  case  is  an  equivalent  resistance. 

With  a  bridge  properly  constructed,  its  coils  being  free  from 
inductance  and  capacity,  it  is  thus  possible  to  make  a  simul- 
taneous measurement  of  the  inductance  and  resistance  to  alter- 
nating currents  of  a  coil  or  piece  of  apparatus. 

To  assist  in  carrying  out  the  necessary  adjustments  in  an 
expeditious  manner,  it  may  be  noted  that  non-magnetic  conduct- 
ors of  small  cross-section,  used  with  currents  of  ordinary  fre- 
quencies, have  practically  the  same  resistance  with  alternating 
as  with  direct  current.  Therefore,  to  save  time,  a  preliminary 
balance  may  be  made  with  direct  current,  using  the  apparatus 
as  an  ordinary  Wheatstone  bridge,  thus  satisfying  the  condition 

7?       -  RM  K 
Lix   -     ~5~  KP. 

KN 

If  the  order  of  magnitude  of  the  inductance  under  measure- 
ment is  entirely  unknown,  one  may  begin  with  RM  =  RN  and 
balance  by  varying  R.  It  may  be  necessary  to  transfer  this 
resistance  to  the  other  side  of  the  bridge  by  changing  the  lead 
from  c  to  e.  Alternating  is  now  substituted  for  direct  current. 
The  detector  will  in  general  give  an  indication  which  must  be 
reduced  to  zero  by  adjusting  the  variable  standard  of  inductance. 
The  chances  are  that  on  account  of  the  limited  range  of  the 
standard,  LP  cannot  be  made  of  such  a  value  as  to  obtain  even  a 
minimum  of  sound  in  the  telephone.  In  this  .case  one  notices 
at  which  end  of  the  scale  the  indication  is  the  smaller,  and  then 
alters  the  ratio  so  that  the  balance  point  will  be  thrown  toward 
the  middle  portion  of  the  scale.  The  bridge  is  then  rebalanced 
for  direct  and  for  alternating  currents.  Two  or  three  trials 
may  be  necessary  in  order  to  obtain  a  good  reading  on  LP. 
If  with  RM  =  RN  the  indication  is  apparently  the  same  at  all 
points  of  the  scale,  a  large  change  should  be  made  in  the  ratio; 
7?  •  /?  1 

for  instance,  to  ~  =  10.     If  this  does  not  give  results,  -~  =  -- 


INDUCTANCE  AND  CAPACITY 


401 


may  be  tried  and  so  on.  Lastly,  a  final  attempt  to  obtain  a 
perfect  zero  indication  of  T  may  be  made  by  altering  R  and  LP 
slightly. 

A  simple  form  of  impedance  bridge  adapted  to  the  determina- 
tion of  inductances  in  terms  of  capacities  and  vice  versa  is  shown 
diagrammatically  in  Fig.  234. 

Equal  ratio  arms  are  employed ;  they  are  advantageous  in  any 
bridge  arrangement  since  their  equality  may  be  checked  at  any 
time  by  simply  reversing  them. 


FIG.  234. — Diagram  of  impedance  bridge  for  comparing  an  inductance  with 

a  capacity. 

The  arms  M  and  N  are  equal  and  they  as  well  as  rx  and  RP 
are  non-reactive,  so  when  the  bridge  is  adjusted  the  arm  X  is, 
in  effect,  non-inductive,  the  inductance  and  capacity  being 
balanced.  Then 

(81o) 


If  Lx  is  to  be  determined  in  terms  of  a  capacity  having  no 
appreciable  losses,  the  balance  is  obtained  by  adjusting  RP  and 
rx.  From  equation  (3 la), 


Lx  = 


I  + 


=  RP  — 


1  +  w'Clr 


(32) 


(33) 


X'X 


If  the  equivalent  capacity  and  insulation  resistance  (Cx  and 
rx)  of  an  imperfect  condenser  are  to  be  determined,  an  adjustable 


402  ELECTRICAL  MEASUREMENTS 

inductance  of  constant  resistance  is  used  at  Lx  and  the  balance 
is  obtained  by  varying  Lx  and  RP. 
From  32  and  33, 

LX  —  CxTx  (Rp   —  RX) 

Rp  =  Rx  +  rx  -  <a*CxLxrx. 
From  these  equations, 


(RP  - 


- 
a      rx  - 


Obviously  the  frequency  must  be  constant  and  of  known  value. 

The  Impedance  Bridge  with  Four  Inductive  Arms.20  —  It  is  de- 
sirable to  inquire  as  to  the  conditions  necessary  for  a  balance 
if  all  four  arms  of  the  impedance  bridge  contain  inductances. 
This  arises  from  the  fact  that  if  very  small  inductances  are  to  be 
compared,  using  currents  of  high  frequency,  the  residual  induct- 
ances existing  in  the  ordinary  double-wound  resistance  coils 
become  of  great  moment.  The  reactances  of  the  bridge  coils 
may  be  positive  or  negative  according  as  the  inductance  or  ca- 
pacity component  preponderates,  and  at  times  may  be  of  the 
same  order  of  magnitude  as  the  reactance  under  measurement. 
In  a  bridge  with  four  inductive  arms, 

ZM  =  RM  + 
ZN  =  RN  + 

ZP  =  RP  + 

Zx  =  Rx  + 
and  at  balance, 

ZM%P  =  ZN 

Substituting, 

RPRM  + 


The  horizontal  component  gives  as  one  condition  for  balance, 

[LNLX  —  LMLP}  co2  +  RpRju  —  RxRN  —  0  (35) 

The  vertical  component  gives  as  the  other  necessary  condition, 

RpLM  —  RNLX  — RxLff  ~h  RuLp  =  0  (36) 


INDUCTANCE  AND  CAPACITY  403 

The  above  results  could  have  been  obtained  directly  from  equa- 
tion (20),  page  389.  As  no  assumption  was  made  in  the  deduction 
of  that  equation  as  to  the  relation  of  iB  to  /,  the  bridge  current 
may  be  assumed  as  sinusoidal, 

is  =  IB  sin  cot. 
Substituting  in  (20)  gives 


[LNLX  -  LMLP]  (-  IB^  sin  «0  +  [-  RPLM  +  R*LX  +  RXLN 

-  RMLP]  (IBu  cos  at)  +  [RNRx  -  RMRP]  (IB  sin  «0  =  0 

which  must  be  true  for  all  values  of  t. 

Consequently  the  coefficients  for  both  the  cosine  term  and  for 

the  collected  sine  terms  must  be  zero. 

.'.  -  [LNLX  -  LMLP]  <o2  +  RNRX  -  RMRP  =  0 
and 

RpLM  —  RNLX  —  RxL<N  H~  RmLp  —  0 

The  sine  terms  correspond  to  the  horizontal  component  in  the 
previous  demonstration  while  the  cosine  term  corresponds  to 
the  vertical  component. 

The  Anderson  Bridge.  —  The  determination  of  an  inductance  in 
terms  of  a  capacity  may  conveniently  be  made  by  means  of  the 
Anderson  bridge.21  This  apparatus  is  a  development  of  the 
bridge  arrangement  given  by  Maxwell.* 

The  connections  are  shown  in  Fig.  235. 

All  the  resistances  except  Rx  are  supposed  to  be  non-inductive. 
The  condenser  is  placed  at  C  and  r  is  an  adjustable  resistance. 

When  variable  currents  are  used,  as  was  originally  intended, 
the  bridge  is  first  balanced  for  steady  currents,  the  battery  cir- 
cuit being  kept  closed.  After  balance  has  been  attained,  the 
capacity  C  and  the  resistance  r  are  adjusted  until  there  is  no 
deflection  of  the  galvanometer  when  the  battery  circuit  is  made 
and  broken.  It  will  be  noted  that  the  adjustment  of  C  and  r 
does  not  disturb  the  steady  current  balance  but  does  affect  the 
rate  at  which  the  potential  of  the  junction  e  rises.  As  the 
initial  values  of  the  potentials  of  6  and  e  are  the  same  and  the 
final  values  are  the  same,  there  will  be  no  current  in  the  de- 

*  "Treatise  on  Electricity  and  Magnetism,"  third  edition,  Art.  778. 


404 


ELECTRICAL  MEASUREMENTS 


lector  at  any  time  if  the  potentials  of  these  two  points  rise  at 
the  same  rate. 

To  determine  the  condition  necessary  for  a  balance,  suppose 
the  steady  current  balance  has  been  attained  and  that  r  has  been 
adjusted  so  that  the  bridge  is  also  balanced  for  variable  currents. 


FIG.  235. — Diagram  for  Anderson  bridge. 
Referring  to  Fig.  235,  by  supposition, 

i0  =  0  continuously 

ic  =  ir. 

From  the  mesh  6,  c,  <i,  e, 

diu 

P.D.a6  =  P.D.M  =  iMRM  =  ^  i  iM 


From  (A),  (B)  and  (C), 


-  (^)    (^*)  RP] 


From  the  mesh  a,  6,  e,  d, 


INDUCTANCE  AND  CAPACITY 


405 


but 


—        _  i 
ir   "    ir 


Substituting  these  values  in  (D)  gives 


Lx  = 


(37) 


The  Anderson  bridge  is  now  used  with  alternating  currents 
and  a  vibration  galvanometer  is  employed  as  the  detector.  This 
arrangement  has  been  used  at  the  Bureau  of  Standards,21  Wash- 
ington, in  much  of  the  recent  and  very  accurate  work  on 
measurements  of  inductance. 


FIG.  236. — Mesh  diagram  for  Anderson  bridge. 

The  necessary  conditions  for  balance  are  shown  below. 
The  impedances  of  the  various  branches  are  denoted  by  Z 
with  the  proper  subscript.     The  mesh  equations  are 

X(ZM  +  Zc)  -  YZG  -  VZC  =  0 
V(ZC  +  Zr  +  ZN)  -  X(ZC  +  Zr)  --  YZr  -  IBZN  =  0 

Y(ZX  +  ZP  +  Zr  +  ZQ)  +  X(ZX  +  ZP  +  Zr)  -  VZr  - 

IBZP  =  0. 
Solving  for  Y,  the  galvanometer  current, 

y  _  ^B\^ M^C^P  "i   £ iuZrZp  -f-  Z M^> N^P  -p  Z M^ xZr  —  Zc 
denominator,  a  function  of  the  impedances 

.*.  for  balance, 


406  ELECTRICAL  MEASUREMENTS 


ZjtfZcZp  ~\~  ZmZj-Zp-}-  ZnfZ^Zp  -f~  Z^Z^Zr  —  ZcZtfZx  =  0.   (38) 

In  the  ideal  case  where  the  coils  of  the  bridge  proper  are  en- 
tirely free  from  inductance  and  capacity, 

ZM  =  RM 

Zx  =  Rx  -\~juLx 

ZP  =  RP 


7    _ 
C~ 


Zr  =  r. 
Substituting  in  (38)  , 

~  +  RMrRP  +  RMRNRP  +  RMRNr  =  -       (Rx  +  juLx)    (39) 


Separating  the  quadrature  components,  the  horizontal  com- 
ponent gives 

Lx  =  RMC  [  r  (l  +  |^)  +  RP]  .  (40) 

The  vertical  component  gives 

RMRP  =  RNRX.  (41) 

Thus  a  perfect  balance  of  the  vibration  galvanometer  implies 
that  both  (40)  and  (41)  are  satisfied. 

To  expedite  matters,  it  is  usual  to  make  a  preliminary  balance 
with  direct  currents,  using  an  ordinary  galvanometer,  thus  satis- 
fying the  condition  (41),  and  then  to  balance  with  alternating 
currents  by  adjusting  r,  the  vibration  galvanometer  being  em- 
ployed. This  method  of  procedure  assumes  that  all  the  resist- 
ances involved  have  the  same  values  for  both  direct  and 
alternating  currents. 

Effect  of  Dissipation  of  Energy  in  the  Condenser.  —  In  the 
demonstration  a  perfect  condenser  has  been  assumed.  As  an 
energy  loss  occurs  in  most  condensers,  it  is  important  to  see  how 
this  loss  will  influence  the  results.  As  previously  shown,  an 
energy  loss  is  equivalent  to  an  increase  of  the  conductance  of 
the  condenser.  Suppose  that  the  condenser  has  been  measured 


INDUCTANCE  AND  CAPACITY 


407 


with  alternating  currents  and  that  its  equivalent  capacity  is 
C,  and  its  equivalent  conductance  is  -^-,  then 


Zc  = 


R, 


1  + .?' 

Substituting  this  value  in  (38), 
RMRcRp 


RCRff(Rx   +  J 


The  horizontal  component  gives 

flxfljr  -  RMRp  =  ^r  [r(RP  +  RN)  +  RNRp]> 
The  vertical  component  gives 

Lx  =  RMC\r(l  +  J^)  +Rp\. 
KNI 

That  is,  the  energy  loss  does  not  complicate  the  measurement  of 
the  inductance. 


FIG.  237. 

Stroude  and  Gates  arrangement  Anderson  bridge,  Fig.  236  redrawn, 

of  the  Anderson  bridge. 

Stroude  and  Gates22  modified  the  Anderson  bridge  by  inter- 
changing the  source  of  current  and  the  detector. 

The  advantage  of  the  rearrangement  is  that  when  the  con- 
ditions are  such  that  r  is  high,  it  is  possible  to  increase  the  applied 
voltage  and  thus  maintain  the  sensitivity  of  the  bridge  by  keeping 
the  bridge  current  at  a  high  value. 

As  the  only  alteration  has  been  to  interchange  the  source  of 
current  and  the  detector,  the  formula  connecting  the  self- 
inductance  and  the  capacity  is  the  same  as  for  the  Anderson 
bridge. 


408 


ELECTRICAL  MEASUREMENTS 


When  very  small  inductances  having  a  magnitude  of,  for 
example,  0.001  henry  are  to  be  measured,  the  residual  induct- 
ances of  the  bridge  coils  must  be  considered.  These  coils  are 
wound  non-inductively,  in  the  usual  understanding  of  the  term, 
but  either  the  inductance  or  the  capacity  effect  may  preponderate. 
The  high  resistance  coils  will  give  the  most  trouble. 

The  Mutual  Inductance  Bridge. — If  variable  or  alternating 
currents  be  used,  a  Wheatstone  bridge  which  has  three  non- 
inductive  arms  and  one  inductive  arm  connot  be  made  to  balance, 
for  the  potentials  at  the  two  ends  of  the  detector  circuit  can 
never  be  in  the  same  time  phase.  A  balance  can  be  obtained, 
however,  by  the  addition  of  an  adjustable  mutual  inductance, 
or  air-core  transformer  of  variable  ratio,  the  secondary  of  which 


FIG.  238. — Mesh  diagram  for  Hughes  bridge. 


is  connected  in  series  with  the  detector  while  the  primary  is 
placed  in  one  of  the  leads  from  the  source  of  supply  to  the  bridge. 
The  primary,  therefore,  carries  the  entire  bridge  current,  and 
the  mutual  inductance  introduces  into  the  detector  circuit  a 
small  e.m.f.  which  is  in  quadrature  with  that  current. 

An  apparatus  so  arranged  was  used  in  1886  by  Professor 
Hughes  and  the  results  obtained  were  given  by  him  in  his  in- 
augural address  on  assuming  the  presidency  of  the  British  Insti- 
tution of  Electrical  Engineers.  The  discussion23  which  fol- 
lowed the  presentation  of  this  paper  should  be  read  by  every 
student  who  has  any  doubts  on  the  question  of  practice  vs. 
theory  plus  practice.  It  is  sufficient  to  say  here  that  on  account 
of  an  inadequate  theory  of  his  bridge  Professor  Hughes  misinter- 
preted the  readings  which  he  obtained.  H.  F.  Weber,  Rayleigh 


INDUCTANCE  AND  CAPACITY  409 

and  Heaviside  showed  that  the  observations  obtained  by  means 
of  the  Hughes  apparatus  are,  when  correctly  reduced,  in  entire 
accord  with  the  accepted  theory  of  induction. 

The  connections  for  this  form  of  bridge  are  shown  in  Fig.  238. 
They  are  much  like  those  for  the  Wheatstone  bridge,  but  in  the 
galvanometer  circuit  is  included  the  secondary  of  the  air-core 
transformer  of  variable  ratio,  the  primary  of  this  transformer 
being  connected  in  the  lead  running  from  the  source  of  current 
to  the  bridge.  The  mutual  inductance  of  the  air-core  transformer 
will  be  represented  by  m.  Assuming  sinusoidal  currents  the 
mesh  equations  are: 

(X  +  Y)  (Zx  +  ZP  +  ZG)  -  XZG  -  IBZP  -  jmaIB  =  0 
X(ZM  +  ZG  +  ZN)  -  (X  +  Y)  ZG  -  IBZN  +  jmuIB  =  0. 

In  respect  to  the  sign  given  to  the  term  involving  the  mutual 
inductance,  in  this  and  other  methods  of  measurement,  it  may 
be  either  positive  or  negative  depending  on  the  manner  in  which 
the  device  is  connected  into  the  circuit.  However,  the  particular 
connection  and  the  corresponding  sign  in  the  equations  must  be 
used  which  will  enable  a  balance  to  be  obtained. 

Solving  the  above  equations  for  F,  the  galvanometer  current, 
and  substituting  the  values  of  the  impedances,  the  arms  M,  N 
and  P  being  non-inductive, 

IB[(Rp  +  jmu)(RM  +  RN)  -  (RN-jmu)(Rx  +  RP  +  JLX<»)] 


denominator 

If  only  the  condition  of  balance  is  required,  it  is  not  necessary  to 
know  the  expression  for  the  denominator.  For  balance,  the 
numerator  must  be  zero  or 

RP  (RM  +  RN)  ~  RN(Rx  +  RP)  ~  m^Lx  +  j[(RM  +  RN)  mco  + 

(Rx  +  RP)  mu  -  LxRNu\  =  0. 

Separating  the  quadrature  components,  the  horizontal  compo- 
nent gives 

RPRM  -  RNRx  =  m^Lx 
and  the  vertical  component  gives 

m(RM  +  RN  +  Rx  +  RP)  =  RNLX. 
In  order  to  obtain  a  balance  both  these  equations  must  be  satisfied. 


410  ELECTRICAL  MEASUREMENTS 

Solving  for  Lx  and  Rx, 

RPRM 


RN 


_  __  , 
RN 


RM  ~\-  RN  H~  RP 


•/// 


2,  ,2 


Rx 


RpR, 


i     i 

R\ 

RM  +  RN 


1    + 


(42) 


(43) 


In  his  paper  Professor  Hughes  treated   his   observations   as 
if    he    were   dealing   with   an    ordinary   bridge,   that   is,   as   if 

,.,        RPRM 
Kx  =      p 

KN 

Heaviside  in  his  examination  of  the  work  of  Professor  Hughes 
pointed  out  that  balance  may  be  obtained  if  the  secondary  of 


FIG.  239. — Mesh  diagram  for  Heaviside  mutual  inductance  bridge. 

the  mutual  inductance  is  introduced  into  one  of  the  main  bridge 
arms  as  well  as  if  it  is  used  in  the  galvanometer  circuit.  Fig.  239 
shows  a  bridge  arranged  in  this  manner;  as  before,  Z  with  the 
proper  subscript  denotes  the  total  impedance  of  the  correspond- 
ing bridge  arm. 

The  mesh  equations  are 

X(ZM  +  ZG  +  ZN)  -  (X  +  Y)  Z0  -  IBZN  =  0 
(X  +  Y)  (Zx  +  ZP  +  ZG)  -  XZ0  -  IBZP  ±  jmu  IB  =  0 


INDUCTANCE  AND  CAPACITY  411 

y  =  i    L  ZpZlM  ~  ZNZx  ±  Jm"  (ZM  +  ZN]          _1 

B  [ZG(ZM  +  ZN+ZX  +  ZP)  +  (ZM  +  ZN)(ZX  +  ZP)\' 

For  a  balance, 

ZPZM  -  ZNZX  ±  jmu  (ZM  +  ZN)  =  0. 


The  balance  arms  of  the  bridge,  M  and  N,  are  non-inductive. 
On  substituting  the  values 

ZM   =  RM 
Z  jv  —  RN 
Zx  —  Rx 
ZP    =  RP 

and  separating  the  quadrature  components  ,  the  horizontal  com- 
ponent gives 

RMRP  =  RNRX.  (44) 

The  vertical  component  gives 

RM  [LP  +  m]  =  RN  [Lx  -  m\.  (45) 

If  ZM  =  ZN  (that  is,  if  a  bridge  with  equal  ratio  arms  is  used), 

Rp  —  Rx 
and 

LX  —  LP  =  2m. 

This  arrangement  is  useful  in  measuring  small  inductances,  for 
as  suggested  by  A.  Campbell,24  a  method  of  differences  can 
be  used  thus  eliminating  the  effects  of  residual  inductances  in  the 
bridge  arms. 

Referring  to  Fig.  239,  the  inductance  to  be  measured  is  inserted 
in  the  gap  n.  m  is  a  variable  mutual  inductance  which  can  be 
adjusted  without  changing  the  inductance  or  the  resistance  of  the 
secondary  circuit.  The  inductance  of  either  the  arm  X  or  the 
arm  P  and  the  resistance  of  P  must  be  adjustable. 

Let  Lx,  LP  and  Rx,  Rp  be  the  values  of  the  inductances  and 
resistances  -when  the  bridge  is  balanced  with  n  short-circuited 
and  the  mutual  inductance  set  at  zero.  Then 

Lx  -  LP  =  0 

Rx  -  Rp   =  0. 


412  ELECTRICAL  MEASUREMENTS 

After  this  preliminary  balance  has  been  obtained,  the  unknown 
inductance  L'x,  of  resistance  R'x,  is  introduced  at  n  and  the 
balance  again  obtained  by  adjusting  m  and  changing  the  variable 
resistance  from  r  to  rf .  Then, 

Lx  +  Lfx  -  LP  =  2m 

Rx  +  R'x  -  [Rp  +  (rf  -  r)]  =  0 

.'.R'x  =r'  -r 
L'x  =  2m. 

Obviously  inductances  from  zero  up  to  a  maximum  of  twice 
the  full  value  of  the  mutual  inductance  can  be  measured. 

In  obtaining  the  inductance  it  is  not  necessary  to  know  the 
values  of  any  of  the  resistances.  The  variable  resistance  r  may 
be  made  of  two  small  and  straight  wires  placed  a  few  millimeters 
apart  and  short-circuited  by  a  bridge  piece.  The  inductance 
of  such  an  arrangement  may  be  calculated,  if  it  is  necessary 
to  allow  for  it. 

The  apparatus  should  be  so  arranged  that  the  equality  of  the 
ratio  arms  may  be  tested  and  their  adjustment  to  exact  equality 
facilitated  by  interchanging  them.  Any  lack  of  equality  affects 
the  value  of  Rx  much  more  than  that  of  Lx. 

Effect  of  Eddy  Currents. — The  fundamental  assumption  on 
which  the  theory  of  any  mutual  inductance  bridge  rests  is  that 
the  current  flowing  in  the  primary  of  the  mutual  inductance  in- 
duces an  e.m.f.  in  the  secondary  which  is  in  quadrature  with  the 
primary  current.  This  assumption  will  be  rendered  invalid  and 
absurd  results  will  be  obtained  with  the  bridge  if  its  construction 
is  such  that  eddy  currents  are  set  up  in  neighboring  masses  of 
metal  or  in  the  wire  of  the  coils  themselves,  if  the  wire  be  large. 
The  effect  becomes  more  pronounced  as  the  frequency  is 
increased. 

The  primary  current  will  induce  an  electromotive  force  in  the 
eddy  current  circuits  which  will  be  in  quadrature  with  itself. 
Assuming  that  the  inductances  of  these  circuits  are  negligible, 
the  eddy  currents  will,  in  turn,  induce  an  electromotive  force  in 
the  secondary  which  will  be  in  quadrature  with  themselves,  and 
therefore  in  opposition  to  the  primary  current.  In  addition, 
there  is  the  direct  induction  from  the  primary  to  the  secondary, 


INDUCTANCE  AND  CAPACITY  413 

which  induces  in  the  secondary  an  e.m.f.  in  quadrature  with  the 
primary  current.  These  two  components  of  the  electromotive 
force  in  the  secondary  must  be  added,  and  obviously  the  result- 
ant electromotive  force  will  not  be  in  quadrature  with  the  primary 
current.  To  illustrate  further,  the  current  in  the  primary, 
Fig.  240,  is  7.  This  is  supposed  to  induce  an  e.m.f.  in  the  sec- 
ondary which  is  represented  by  —  jmul.  Let  e  represent  the 
,path  of  the  eddy  current ;  its  mutual  inductance  with  respect  to 
the  primary  is  mi  and  with  respect  to  the  secondary  is  w2. 


FIG.  240.  —  Pertaining  to  eddy  current  errors  in  mutual  inductance  bridge. 
The  e.m.f.  induced  in  the  eddy-current  circuit  by  I  will  be 
Ee  =  —jmiwl. 

The  corresponding  current  will  be 

jmiul 

"  Re  +  juLe' 

Ie  will  induce  an  e.m.f.  in  the  secondary,  given  by 


Re2  +  C02L2e 

To  obtain  the  total  e.m.f.  induced  in  the  secondary,  E'e  must  be 
added  to  —  jmwl.     Then 

E=   - 

If  Le  is  negligible,  the  eddy  current  induces  a  component  in 
quadrature  with  that  due  to  the  primary  current  and  of  a  mag- 


414  ELECTRICAL  MEASUREMENTS 

nitude  depending  on  the  square  of  the  frequency,  hence  its  in- 
creasing importance  at  high  periodicities.  This  shows  that  all 
massive  metal  frames  and  metal  fastenings  must  be  avoided. 
The  coils  must  be  wound  with  a  conductor  made  up  of  small 
strands  which  are  insulated  from  one  another.  For  economy  of 
space,  enameled  wire  may  be  used. 

Wilson  Method  for  Measuring  Inductance. — In  this  method 
the  reactive  component  of  the  potential  difference  between  the 
terminals  of  the  unknown  inductance  is  measured  by  a  quadrant 
electrometer.25  The  connections  are  shown  in  Fig.  241. 

The  two  sets  of  quadrants  are  connected  to  the  terminals 
of  the  unknown  inductance.  One  end  of  the  needle  circuit  is 
attached  to  Rx ,  preferably  at  the  middle.  T  is  an  air-core  trans- 
former of  mutual  inductance,  m,  and  V  an  electrostatic  voltmeter 


A  m  ^  -  d  -  ^ 

FIG.  241.  —  Connections  for  Wilson  method  for  measuring  inductance. 

% 

for  determining  the  potential  of  the  needle.     A  is  an  ammeter 
for  measuring  the  main  current. 

When  applied  to  this  case,  the  elementary  formula  for  the 
deflection  of  the  quadrant  electromotor  becomes 


d  =  Rxi  +  Lx  -^  - 

Let  the  readings  of  the  electrostatic  voltmeter  and  of  the 
ammeter  be  V  and  7.     Assuming  sinusoidal  currents, 


INDUCTANCE  AND  CAPACITY  415 


and  only  the  reactive  component  produces  a  turning  moment. 
Then 


\dt/ 
:.  D  =  ZuKVILx     or    Lx  =  TTJF^TJ  (46) 


This  method  may  be  applied  to  the  measurement  of  small 
inductances  having  a  large  current-carrying  capacity  and  a  small 
resistance;  for  example,  it  has  been  applied  to  shunts  such  as  are 
used  for  alternating  current  measurements. 

The  secondary  of  the  air-core  transformer  may  be  the  secondary 
of  an  ordinary  induction  coil.  The  primary  may  be  wound  to 
have  a  number  of  turns  depending  on  the  current  to  be  dealt 
with. 

The  Measurement  of  Inductances  Containing  Iron. — The  pre- 
ceding methods  are  adapted  to  the  measurement  of  coils  with  air 
cores,  for  in  that  case  the  self-inductance  is  constant,  as  has  been 
assumed  in  all  the  demonstrations.  If  the  coils  have  iron 
cores,  then  owing  to  the  dependence  of  the  permeability  on  the 
degree  of  saturation  of  the  iron,  the  self-inductance  is  no  longer 
constant  but  varies  during  the  cycle. 

In  such  cases  the  effective  inductance  may  be  determined  from 
measurements  of  the  applied  voltage,  current,  frequency  and 
power. 

1?  (47) 

The  current  should  be  adjusted  to  the  value  it  has  in  the  ordinary 
use  of  the  apparatus.  With  telephonic  apparatus  it  is  possible 
to  obtain  satisfactory  results  by  bridge  methods,  for  the  satura- 
tion is  so  low  that  the  permeability  is  practically  constant. 

Measurement  of  Mutual  Inductance. — An  obvious  method  of 
determining  the  mutual  inductance  of  two  coils  is  to  connect 
them  in  series  and  to  measure,  by  any  convenient  method,  the  net 
self -inductance  of  the  combination;  then  to  reverse  one  of  the 


416  ELECTRICAL  MEASUREMENTS 

coils  and  again  measure  the  net  inductance.'  One  measurement- 
gives  the  sum,  the  other  the  difference  of  the  mutual  and  self- 
inductance  effects.  If  the  two  net  inductances  are  L'  and  L", 
and  the  self-inductances  of  the  coils  are  LI  and  L2,  respectively, 

L'    =  Li  +  L2  +  2m 
L"  =  Li  +  L2  -  2m. 

Consequently  the  mutual  inductance  is  given  by 

T  '         T  " 

m  =  L-^~  (48) 

Maxwell  Method  of  Comparing  Mutual  Inductances. — The 

connections  necessary  for  coniparing  two  mutual  inductances 
by  Maxwell's  method  are  shown  in  Fig.  242  where  it  is  indicated 


ra.r 


FIG.  242. — Mesh  diagram  for  Maxwell  method  of  comparing  mutual 
inductances. 

that  alternating  currents  replace  the  variable  currents  assumed 
in  the  original  demonstration.*  The  two  mutual  inductances 
are  mx  and  mP ;  Zx  and  ZP  are  the  impedances  of  the  respective 
meshes  omitting  the  detector;  L'  is  a  variable  self-inductance 
which  can  be  used  in  series  with  either  mx  or  mP.  Its  value  need 
not  be  known. 

The  mesh  equations  are 

XZX  -  YZG  -  jwmxIB  =  0 
XZP  +  Y(ZP  +  Z0)  -  jumPIB  =  0 
from  which  the  detector  current  is 


V  - 

~ 


xmp  ~     pmx 

LZfZ&  +  Zx(ZP  +  Z 


*  "Treatise  on  Electricity  and  Magnetism,"  third  edition,  Art.  775. 


INDUCTANCE  AND  CAPACITY  417 

In  order  that  the  detector  current  may  be  zero, 
ZxmP  =  ZPmx. 

When  the  values  of  Zx  and  ZP  have  been  substituted  and  the 
quadrature  components  separated,  the  horizontal  component 
gives 

mx  =  rx 
mP       rP 
or 

mx  =~mx  (49) 

and  the  vertical  component  gives 

—  =  Lj~-  (50) 

mP       LP 

As  (50)  must  be  satisfied  and  the  self-inductances  of  the 
secondaries  of  the  mutual  inductances  cannot  be  varied  at  will, 
it  is  necessary  to  include  the  variable  self-inductance  L'. 

If  the  source  of  current  and  the  detector  are  interchanged  and 
the  secondaries  of  the  mutual  inductances  are  connected  in 
opposition,  the  arrangement  will  be  balanced  if  the  two  sec- 
ondary e.m.fs.  are  equal  at  every  instant;  that  is,  when 

_.-   V_  .     V 

.*.  — —  =  -£  as  before. 
mP       LP 

A  disadvantage  of  the  method  just  given  is  that  rx  and  rP 
include  the  resistances  of  the  copper  secondaries  of  the  mutual 
inductances;  they  must  be  determined  by  a  separate  bridge 
measurement. 

A.  Campbell24  has  developed  the  method  so  that  these  re- 
sistances are  replaced  in  the  formula  for  mx  by  those  of  care- 
fully calibrated  bridge  coils.  The  connections  are  shown  in 
Fig.  243.  Here  mP  is  a  variable  standard  of  mutual  inductance; 
the  inductance  and  the  resistance  of  its  primary  circuit  are 
fixed. 

In  carrying  out  the  measurement  the  switches  are  first  thrown 
to  position  1,  the  desired  values  of  RM  and  RN  unplugged  and  a 

27 


418 


ELECTRICAL  MEASUREMENTS 


balance  obtained  by  adjusting  Z/.  The  arrangement  is  then 
a  simple  impedance  bridge,  and  at  balance 

Z M    _    Z  ff  Z M    _    Zx   T  Z M 

Zx        Zp  Z  N       Z  ff  T  Zp 

The  opposed  secondaries  of  the  mutual  inductances  are  next 
introduced  into  the  detector  circuit  by  throwing  the  switches  to 
position  2  and  a  balance  obtained  by  adjusting  mP. 


FIG.  243. — Connections    for    Campbell    method    of    comparing    mutual 

inductances. 

At  balance  the  two  secondary  e.m.fs.  must  be  equal,  or 
.     umxV  .     umpV 

~  3  ~7        "l       V         ==  3  ~r/  I       V 

AX    T"  AM  A  ff    -J-  £JP 

.     mx         Zx  ~\-  ZM         ZM         RM 


mP 


Z  ff  -\- 


ZN 


and 


R 


(51) 


Measurement  of  Mutual  Inductance  in  Terms  of  Capacity.— 

The  connections  for  the  Carey  Foster  method  of  comparing  a 
mutual  inductance  with  a  capacity,  as  modified  by  Heydweiller,26 
are  shown  in  Fig.  244.  C  is  a  condenser;  r,  Ri  and  Rz  are 
non-inductive  resistances.  r2  is  the  resistance  and  L2  the  self- 
inductance  of  the  secondary  of  the  mutual  inductance. 
The  impedances  are 


INDUCTANCE  AND  CAPACITY 

The  mesh  equations  are 

X(ZC  +  ZG  +  ZO  -(X+Y)Z0-  /*Zi,  =  0 

(X  +  Y)  (Z2  +  ZG)  -  XZC  ±  jumxIB  =  0. 
Solving  for  the  galvanometer  current, 

Z\ZG  -f~  \Zz  ~h  ZG)  (Zc  -\-Zi) 


419 


FIG.  244. — Connections  for  measurement  of  mutual  inductance  in  terms  of 

capacity. 

Therefore  the  equation  for  balance  is 


)"  ^A  * 

~c  =  J 


On  separating  the  quadrature  components  the  horizontal  compo- 
nent gives 


r2) 


the  vertical  component  gives 


L2  = 


Ri 


(52) 


(53) 


The  adjustment  of  R2  and  C  does  not  disturb  the  second  condition 
for  balance,  and  an  adjustment  of  r  does  not  disturb  the  first 
condition.  The  two  adjustments  are  thus  independent  and  the 
arrangement  a  convenient  one.  The  resistance  Ri  should  have 
a  large  current-carrying  capacity.  From  (53)  it  is  seen  that  if  the 
resistance  r  is  not  present,  mx  =  LZ-  This  is  the  lowest  usable 
value  of  L2.  If  the  inductance  in  the  branch  2  is  below  this  value 
it  must  be  increased  by  adding  an  inductive  coil.  In  Carey  Fos- 


420 


ELECTRICAL  MEASUREMENTS 


Deflecting 
'   Coil 


ter's  original  method,  the  resistance  r  was  absent  and  variable 
currents  were  used. 

SOURCES  OF  CURRENT 

In  discussing  all  of  these  bridge  methods  sinusoidal  currents 
have  been  assumed.  If  a  telephone  is  to  be  used  as,  a  detector 
and  the  bridge  settings  are  to  be  made  with  precision  it  is  neces- 
sary that  this  assumption  be  closely  fulfilled.  As  far  as  the 
balancing  is  concerned,  when  a  vibration  galvanometer  is  used 
the  wave  form  is  not  so  important.  There  are  cases,  however, 
where  the  balance  depends  on  the  frequency,  so  it  is  highly  desir- 
able that  the  source  of  current  be  one  which  naturally  gives  a 

sinusoidal  wave. 

Vreeland  Oscillator. — As  the 
amount  of  power  required  is 
generally  small,  one  is  not  limited 
to  the  use  of  a  dynamo  and  for 
bridge  work  the  best  source  of 
current  is  the  Vreeland  Sine 
Wave  Oscillator.28 

The  wave  form  obtained  from 
the  device  is  accurately  sinu- 
soidal and  the  frequency,  which 
can  be  varied  from  about  160  up 
to  4,000  cycles  per  second,  is 
constant  for  any  particular  setting  of  the  apparatus. 

The  device  is  shown  diagrammatically  in  Fig.  245  and  as 
actually  constructed  in  Fig.  246.  The  arrangement  is  such  that 
sinusoidal  oscillations  of  the  desired  frequency  are  set  up  in  the 
primary  of  an  air-core  transformer,  the  secondary  of  which  is 
connected  to  the  bridge. 

The  large  glass  bulb  G  is  the  container  for  a  mercury  vapor  arc 
in  vacuo.  The  mercury  cathode  is  at  D  and  two  carbon  anodes 
are  at  A  and  B.  H  is  any  convenient  source  of  direct  current. 
.Ri  and  R%  are  controlling  resistances  and  Z/i  and  L2  are  two 
reactors  which  tend  to  prevent  rapid  changes  of  the  direct  current 
which  flows  from  H.  In  starting  the  arc  an  auxiliary  electrode 
F  is  used  and  by  closing  the  switch  K  and  tilting  the  container 
Gj  the  mercury  in  F  and  that  in  D  are  brought  into  contact. 


FIG.  245. — Diagram  for  Vreeland 
sine  wave  oscillator. 


INDUCTANCE  AND  CAPACITY  421 

The  oscillating  circuit  ACB  contains  an  adjustable  condenser, 
C,  and  the  inductance  of  the  two  deflecting  coils,  and  can  there- 
fore be  tuned.  The  secondary  coil  from  which  the  current 
is  taken  to  the  bridge  is  in  the  magnetic  field  of  the  deflecting 
coils  which  thus  serve  the  double  purpose  of  causing  the  arc  to 
oscillate  between  D  and  A  and  D  and  B  and  of  acting  as  the 
primary  of  the  air-core  transformer. 


FIG.  246. — Vreeland  sine  wave  oscillator. 

If  the  arrangement  were  perfectly  symmetrical  the  arc  would 
divide  equally  between  the  two  anodes,  the  potentials  of  A  and 
B  would  be  equal  and  no  current  would  flow  through  the  circuit 
ACB.  If  from  any  cause  the  arc  to  B  is  trie  stronger,  this  equality 
of  potentials  is  disturbed,  the  potential  of  B  is  lowered  relatively 
to  that  of  A,  and  a  current  begins  to  flow  in  the  oscillating  circuit 


422 


ELECTRICAL  MEASUREMENTS 


ACB.  The  arcs  are  in  the  field  of  the  deflecting  coils  in  the  cir- 
cuit ACB  and  these  coils  are  so  wound  that  they  still  further 
deflect  the  arc  away  from  A  and  toward  B.  When  the  condenser 
is  fully  charged,  the  current  in  the  deflecting  coils  ceases  and  the 
arcs  begin  to  return  toward  their  first  condition.  The  condenser 
discharges  and  by  means  of  the  deflecting  coils  the  arcs  are 
forced  toward  A. 

The  frequency  with  which  the  condenser  is  charged  and  dis- 
charged depends  upon  the  inductance  and  capacity  and  is  given  by 


tt 

\Vc 


~  27r\/L 

The  variations  in  frequency  are  obtained  by  adjusting  the 
capacity  C.  The  inductance  L  depends  to  a  certain  extent  upon 
the  positions  of  the  two  Reflecting  coils.  It  is,  therefore,  neces- 
sary to  determine  the  frequency  after  the  apparatus  has  been  set 
up.  The  calibration  is  readily  made.  The  current  from  the 
secondary  is  led  through  a  telephone  and  the  note  obtained 
compared  by  the  method  of  beats  with  that  of  a  standard 
tuning  fork.  After  this  calibration,  the  frequency  corresponding 
to  any  other  capacity  is  readily  calculated. 

Care  must  be  taken  in  locating  the  apparatus,  which  sets  up 
a  considerable  stray  field.  When  a  telephone  is  used  as  the 
detector  the  apparatus  must  be  so  set  up  that  the  note  which 
the  oscillator  emits  does  not  disturb  the  observer. 

The  Microphone  Hummer.— If  it  is  not  necessary  to  work  at 
a  definite  frequency,  a  simple  microphone  hummer,  as  shown  in 
Fig.  247,  is  a  convenient  source  of  current. 


Transmitter        Receiver 


"I1  ' 

5  Dry 

Ii 
1  >\A/\ 
IWV 

1    1—                                               —  ^-v 

Switch                               \ 
Cells 

iduction  Coil 

^  tr 

3 

nrwwvt 

1 

To  Bridge 

FIG.  247. — Diagram  for  simple  microphone  hummer. 


INDUCTANCE  AND  CAPACITY 


423 


This  arrangement  gives  a  sharp  tone  which  enables  the  null 
point  to  be  accurately  determined.  The  frequency,  however,  is 
somewhat  uncertain  and  is  controlled  by  the  battery  strength  and 
the  distance  between  the  transmitter  and  receiver  diaphragms. 
This  simple  arrangement  has  been  improved  by  A.  Campbell  so 
that  a  constant  frequency  may  be  obtained;  this  apparatus  is 
shown  in  Fig.  248. 


FIG.  248A. 


Microphone] 


FIG.  248. — Campbell  microphone  hummer. 

The  receiver  diaphragm  is  replaced  by  a  bar  of  mild  steel  2.5 
cm.  in  diameter  and  23.7  cm.  long  (for  a  frequency  of  2,000). 
The  bar  is  supported  at  its  nodal  points  on  two  adjustable  bridge 
pieces.  The  frequency  may  be  altered  by  changing  the  bar  and 
at  the  same  time  altering  the  capacity  of  the  condenser  so  that 
800,  1,000  or  2,000  periods  per  second  may  be  attained.  The 
hummer  is  started  by  lightly  striking  the  bar  and  then  adjusting, 
by  the  milled  head  F,  the  height  of  the  magnet  E,  which  main- 
tains the  vibration.  To  prevent  electrostatic  disturbances,  the 
winding  D  is  covered  with  an  electrostatic  shield  which  may  be 
connected  to  earth. 

When  using  the  hummer  for  measuring  small  capacities  or 


424  ELECTRICAL  MEASUREMENTS 

high  inductances,  it  is  advantageous  to  connect  it  to  the  bridge 
through  an  auxiliary  tuning  circuit  as  shown  in  the  diagram,  where 
K  is  a  subdivided  condenser  and  L  an  adjustable  inductance. 
The  values  of  these  are  adjusted  to  produce  resonance  with  the 
fundamental  frequency  of  the  hummer  and  by  this  method  it  is 
quite  possible  to  obtain  pressures  up  to  50  or  100  volts  at  the 
bridge  terminals  if  only  a  small  amount  of  current  is  desired. 

Electrical  Resonators. — The  most  obvious  method  for  obtain- 
ing the  current  is  by  the  use  of  small  dynamos  of  high  frequency, 
but  difficulties  present  themselves  because  of  harmonics  in  the 
wave  forms.  For  high  periodicities  it  is  necessary  to  use  a 
telephone  as  a  detector,  and  to  obtain  a  good  null  point  a  pure 
sine  wave  is  necessary.  This  may  be  attained  by  eliminating, 
by  means  of  electrical  resonators  or  barriers,  all  but  the  harmonic 
of  the  desired  frequency.  It  is  to  be  kept  in  mind  that  resonating 
arrangements  partially  eliminate  all  but  a  selected  harmonic. 

If  an  efficient  selective  device  be  used,  a  complex  wave  form 
may  become  advantageous,  for  the  harmonic  of  the  desired 
frequency  may  be  selected,  for  instance,  the  fundamental,  the 
third,  the  fifth,  and  so  on;  and  one  machine  run  at  a  constant 
speed  will  serve  for  measurements  at  a  number  of  different 
frequencies. 

Fleming  and  Dyke  Resonator. — Fleming  and  Dyke  in  their 
researches  oh  the  power  factor  and  conductivity  of  dielectrics18 
used  a  small  dynamo  having  a  normal  frequency  of  about  900 
cycles  per  second.  The  wave  form  of  this  machine  was  far  from 
sinusoidal,  the  third  and  fifth  harmonics  being  very  pronounced. 
By  the  use  of  a  resonator,  they  were  able  to  select  and  use  in  their 
bridge  either  the  fundamental  of  920  periods  per  second,  the 
third  (2,760)  or  the  fifth  harmonic  (4,600),  the  machine  being 
operated  at  a  constant  speed. 

Referring  to  Fig.  249,  Ci  is  an  adjustable  paraffined  paper 
condenser  of  20  microfarads  capacity.  The  adjustable  induc- 
tance L]  is  made  by  winding  single  layer  coils  of  No.  14  wire  on 
two  pasteboard  tubes,  one  of  which  can  be  slipped  within  the 
other.  The  two  coils  are  connected  in  series  by  a  flexible  wire 
and  the  inductance  is  adjusted  by  inserting  the  inner  tube  to  a 
greater  or  less  extent.  Three  of  these  inductances  may  be  neces- 
sary to  cover  the  range  of  the  fundamental,  the  third  and  the 


INDUCTANCE  AND  CAPACITY 


425 


fifth  harmonics.  As  in  all  electrical  resonators",  the  ohmic  resis- 
tance of  these  coils  must  be  kept  low  if  the  resonant  point  is  to 
be  sharply  defined. 

The  relation  between  the  inductance  and  capacity  necessary 
to  resonate  a  harmonic  of  frequency  /  is  given  by 


or  if  C  be  in  microfarads  and  L  in  millihenrys, 

5,033 

/    ~    .  /r~ri 


Adjustable 


Adjustable 

Adjustable  Inductance 
Condenser  and  Air  Core 

Transformer 


Bridge 


Second 

Adjustable 

Inductance  and 

Air  Core  Tr.anslo.rmer 


FIG.  249. — Diagram  for  Fleming  and  Dyke  resonator. 

The  capacities  and  inductances  used  by  Fleming  and  Dyke  were 
as  follows: 


Frequency 

Li  in  millihenrys 

Ci  in  microfarads 

920 

1.5 

20 

2,760 

0.81 

4 

4,600 

0.60 

2 

To  obtain  a  pure  sine  wave  it  was  found  necessary  to  use  a  second 
resonator  electromagnetically  coupled  with  the  first  by  an  air- 
core  transformer  formed  by  thrusting  a  secondary  coil  wound 
on  a  paper  tube,  T\,  into  the  first  adjustable  inductance,  LI.  The 
capacities  used  in  this  second  resonator  circuit  could  be  varied 
from  0.25  to  8.25  microfarads.  As  indicated,  the  bridge  cur- 
rent is  derived  from  a  second  air-core  transformer,  its  secondary, 
T2)  being  inserted  in  L2. 

DEVICES  FOR  MAINTAINING  CONSTANT  SPEED 

In  many  methods  of  measurement,  particularly  when  dealing 
with  inductances  and  capacities,  it  is  necessary  accurately  to 


426 


ELECTRICAL  MEASUREMENTS 


control  the  speed  of  the  electric  motor  which  drives  the  contact- 
making  device  or  the  alternator  which  furnishes  the  current.  It 
is  presupposed  that  the  voltage  of  the  supply  is  kept  constant. 
Hand  regulation  may  be  employed  if  some  very  sensitive  form  of 
detector  be  used  which  will  at  once  make  evident  a  change  of 
speed,  but  in  careful  work  this  necessitates  an  additional  observer 
whose  only  duty  is  to  note  the  speed  indicator  and  keep  the  con- 
trol rheostat  adjusted.  Therefore,  some  arrangement  which 
will  be  automatic  in  its  action  is  required. 

The  Giebe  Speed  Regulator.29 — A  shunt-wound  direct-current 
motor  may  be  controlled  by  a  form  of  centrifugal  governor  devised 
by  Giebe. 


Supply 
FIG.  250. — Giebe  speed  regulator. 

Fig.  250  shows  the  diagram  of  the  circuits  and  a  general  view 
of  the  governor.  The  resistance  X  is  for  the  rough  adjustment 
of  the  speed. 

When  the  speed  rises  too  high,  the  governor  short-circuits  a 
resistance  in  the  field  circuit  and  thus  decreases  the  speed. 

Referring  to  Fig.  251,  the  frame  D  carries  the  mechanism  and  is 
rigidly  attached  to  the  shaft  R  which  is  directly  connected  to  the 
motor.  The  electrical  connections  to  the  contacts  KI  and  K2 
are  made  through  the  slip  rings  V.  The  weight  P  slides  on  a 


INDUCTANCE  AND  CAPACITY 


427 


guide  wire  W  and  must  move  without  appreciable  friction;  it 
is  drawn  inward  by  the  spiral  springs,  F,  the  tension  of  which 
may  be  regulated.  When  the  motor  is  started  the  centrifugal 
force  causes  the  weight  to  move  out  in  opposition  to  the  control 
exercised  by  the  springs.  If  the  speed  be  high  enough,  contact 
between  KI  and  Kz  will  be  made  and  the  resistance  short-cir- 
cuited. The  motor  then  slows  down  a  little  and  the  contact 
is  broken;  the  speed  then  rises  and  the  cycle  is  repeated.  Thus 
the  speed  is  "kept  constant,  subject  to  very  slight  oscillations 
about  its  mean  value. 

The  position  of  the  piece  Q 
to  which  the  rear  ends  of  the 
springs  are  attached  may  be  ad- 
justed by  the  micrometer  screw 
T  (pitch  1  mm.)  and  when  prop- 
erly adjusted  may  be  clamped 
in  position  on  the  rods  SS.  The 
platinum  contact  K}}  which  is 
carried  by  a  flat  spring  of  mode 
rate  strength,  is  insulated  and 
mounted  on  the  weight  P  and  is 
connected  to  one  of  the  slip 
rings  by  a  flexible  wire.  The 
contact  K2  is  a  flat  plate  of 
platinum  and  the  bar  H  which 
carries  it  may  be  set  at  any 
desired  distance  from  the  axis. 


FIG.    251.— Details   of    Giebe    speed 
As  the  shaft  runs  through  the  regulator, 

device  two  springs  are  used  as  indicated  in  the  smaller  figure. 
It  is  obvious  that  on  account  of  the  shaft  the  center  of  gravity 
of  the  weight  can  never  be  brought  to  the  axis  of  rotation.  Let 
a'  be  its  minimum  possible  distance  from  the  center  of  the  shaft, 
M  be  the  mass  of  the  weight  and  C  the  constant  of  the  springs, 
that  is,  the  force  in  dynes  necessary  to  extend  the  springs  1  cm. 
Let  r  be  the  distance  of  the  center  of  gravity  of  the  weight  from 
the  center  of  the  shaft  when  the  latter  is  rotating  with  an  angular 
velocity  co.  It  will  be  assumed  that  the  springs  have  been  given 
an  initial  tension  TI,  that  is,  when  the  device  is  at  rest  in  a 
horizontal  position  and  the  weight  is  in  contact  with  the  shaft,  a 


428  ELECTRICAL  MEASUREMENTS 

tension,  TI,  has  been  applied  to  the  springs  by  means  of  the 
micrometer  screw. 

When  the  angular  velocity  is  co  and  the  center  of  gravity  is  r 
cm.  from  the  axis,  the  centrifugal  force  will  be 


Kc  = 
and  the  tension  on  the  springs  will  be 

Ks  =  C(r  -  a'}  +  T, 
At  equilibrium  Kc  =  Ks  and 

=  C(r  -  a')  +  T 


The  equilibrium  may  be  stable,  neutral,  or  unstable,  depending 
on  the  initial  tension  T\.  For,  suppose  that  at  some  instant 
when  the  center  of  gravity  of  the  weight  is  distant  r  from  the 
axis,  KG  happens  to  be  equal  to  Ks.  If  the  weight  is  given  a 
slight  displacement  outward,  5r, 

dKc       dr         -dKs  Cdr  dr 

~i^~  =  —  and 


r  c     \KS   '     C(r  -  a')  +T* 

I  I  Ct  ^ 


T 

-Q  is  the  initial  extension  of  the  spring.     It  will  be  denoted  by 

e1 ';  then 


Ks      r-  (ar  -  e'} 

If  a'  is  greater  than  e'  the  denominator  of  the  expression  for 
bK  fiK  &K 

^~  is  less  than  r,  -j~—  >  -~—  and  the  weight  will  return  toward 
J±s  AS          A  c 

its    original    position,    that    is,    the  equilibrium  is  stable.     If 

ft  K       &JC 
af  =  ef ,  then  ~JF~.**~jr~    and    the   equilibrium   is   neutral.     If 

&K       &K 
a'  is  less  than  ef  the  denominator  is  greater  than  r  and  -«r^<~F~~< 

AS  AC 

In  this  case,  the  weight  will  suddenly  fly  outward  to  the  extent 
of  its  travel,  the  spring  being  insufficient  to  make  it  return  to  its 
original  position.  This  is  the  case  of  unstable  equilibrium. 

If  the  springs  be  given  increasing  tension  the  equilibrium 
remains  stable  until  7\  =  Caf  or  e'  =  a',  that  is,  until  the  tension 
is  that  which  would  bring  the  center  of  gravity  of  the  weight  to 


INDUCTANCE  AND  CAPACITY  429 

the  center  of  the  shaft  if  the  motion  of  the  weight  in  that  direc- 
tion were  not  limited.  This  may  be  called  the  critical  value  of 
the  tension,  since  if  it  is  exceeded,  the  weight  will  suddenly  fly 
outward. 

While  the  device  may  be  operated  with  any  one  of  the  three 
adjustments  implied  above,  it  is  most  sensitive  and  regulates 
best  when  the  tension  is  near  its  critical  value.  Referring  to  the 
equation  of  equilibrium, 

McuV  =  C(r  -  a')  +  7\ 
or 

M 


If  Caf  =    Ti  or,  what  is  equivalent,  if  a'  =  e', 


This  may  be  called  the  critical  speed,  since  for  any  higher  speed 
the  equilibrium  is  unstable. 

Why  the  apparatus  regulates  most  satisfactorily  in  the  neighbor- 
hood of  the  critical  speed  becomes  evident  if  values  of  co  and  r  be 
plotted;  this  has  been  done  in  Fig.  252,  two  values  of  e'  being 
used. 

It  has  been  assumed  in  Fig.  252  that  the  construction  of  the 
regulator  is  such  that  the  center  of  gravity  of  the  weight  can  never 
be  nearer  the  axis  than  3  cm.  or  more  distant  than  6  cm.  It  is 
seen  that  as  the  critical  speed  is  approached  the  change  in  the 
position  of  the  weight  for  a  given  increase  in  the  angular  velocity 
becomes  vastly  increased.  This  means  a  corresponding. increase 
in  the  sensitiveness  of  the  apparatus. 

If  a'  >  e'  the  weight  arrives  at  its  ultimate  position  slowly  and 
the  contact  of  K\  and  K%  may  be  uncertain.  If  a'  <  e'  the  motion 
is  sudden  and  the  pressure  between  the  contacts  considerable. 
For  the  best  results  e'  should  be  slightly  larger  than  a',  that  is, 
the  initial  tension  on  the  springs  should  be  such  that  the  weight  is 
in  unstable  equilibrium  at  the  speed  which  it  is  desired  to 
maintain. 

Any  given  regulator  has  only  one  speed  at  which  it  works  with 

entire  satisfaction,  that  is,  at  co  =  A  /—• 

\M 


430 


ELECTRICAL  MEASUREMENTS 


If  it  is  desired  to  regulate  the  motor  at  some  other  speed 
either  C  or  M  must  be  altered. 

To  adjust  the  tension  of  the  springs  so  that  the  center  of  gravity 
is  in  the  proper  initial  position,  that  is,  to  give  a'  —  e'  its  correct 
value,  it  is  necessary  to  experiment  with  the  completed  appara- 


89  90  91  92       w 

Angular  Velocity 

850  _  870       t      880 

Revolutions  per  Minute 


FIG.  252.  —  Pertaining  to  Giebe  speed  regulator. 

tus.     Tests  show  that  the  regulator  will  keep  the  speed  constant 
to  about  ;Ho>ooo  Part  of  its  mean  value. 


The  Leeds  and  Northrup  Automatic  Speed  Controller. — The 

constant  speed  necessary  for  driving  secohmeter  devices,  as 
well  as  sufficient  energy  (about  150  watts  at  70  volts)  for  most 
of  the  measurements  of  inductance  and  capacity  made  in  an  ordi- 
nary laboratory,  may  be  conveniently  obtained  by  use  of  a  device 


INDUCTANCE  AND  CAPACITY 


431 


of  the  Leeds  &  Northrup  Co.,  in  which  a  small  rotary  converter, 
or  motor-generator  set  is  controlled  by  an  electrically  operated 
tuning  fork. 

The  connections  of  the  apparatus  are  shown  in  Fig.  253.  The 
circuits  necessary  for  driving  the  fork  are  shown  by  dotted  lines 
and  the  synchronizing  circuits  by  solid  lines. 


D.C.Side 
Motor  Generator 
Set 


Diagram  for  Leeds  and  Northrup  speed  controller. 


Electrically  driven  tuning  fork. 
FIG.  253. 

The  speed  of  the  direct-current  motor  is  first  regulated  by  a 
rheostat  in  the  armature  circuit  so  that  the  motor  tends  to  drive 
the  alternator  at  a  speed  about  10  per  cent,  above  synchronism. 

If  it  is  desired  to  maintain  a  frequency  of  60  cycles,  for  instance, 
the  fork  is  regulated  by  means  of  the  movable  weights  W  and  the 
movable  spring  S,  which  gives  a  fine  adjustment,  until  its  rate  is 


432  ELECTRICAL  MEASUREMENTS 

60  complete  vibrations  a  second.  When  the  alternator  gives 
exactly  60  cycles,  the  contacts  KI  and  K2  will  be  made  at  a  definite 
point  in  the  voltage  wave  and  no  effect  will  be  produced.  If, 
however,  the  direct-current  motor  tends  to  speed  up  and  drive 
the  alternator  a  little  above  synchronism,  the  contacts  K\  and 
Kz  are  made  when  the  electromotive  force  has  a  higher  value 
and  a  larger  current  will  flow  from  the  secondary  of  the  trans- 
former through  the  lamp.  This  throws  an  additional  load  on  the 
'  motor,  the  magnitude  of  which  is  dependent  upon  the  departure 
from  synchronism. 

As  there  is  a  resistance  in  the  armature  circuit  of  the  motor, 
this  load  slows  the  machine  down  and  brings  it  back  to  synchron- 
ism. Thus  by  a  series  of  small  and  rapidly  applied  loads  (120 
a  second)  the  motor  is  held  in  check.  If  the  motor  tends  to  slow 
down,  the  contact  is  made  when  the-  voltage  is  smaller,  the  load 
on  the  motor  is  decreased  and  the  speed  maintained  constant. 
Motors  up  to  1  kw.  may  be  controlled  in  this  manner.  As  with 
all  adjustable  tuning  forks,  the  weights  W  should  be  set  exactly 
opposite  each  other.  The  adjustment  of  the  contacts  is  impor- 
tant. When  the  fork  is  at  rest,  the  contact  springs  should  be 
equally  distant  from  K\  and  K2,  about  ^2  m-  To  reduce  the 
sparking,  the  condensers  Ci  and  C2  are  shunted  around  the  breaks 
at  KI,  Kz,  and  K%.  The  binding  posts  at  C\  allow  the  insertion 
of  additional  capacity  around  the  breaks  KI  and  K^,  if  this  be 
found  necessary.  The  transformer  is  used  in  order  to  separate 
entirely  the  load  from  the  synchronizing  current,  this  being 
necessary  in  order  to  avoid  leakage,  etc.  Usually  a  1 : 1  ratio  is 
employed,  but  when  the  larger  sized  motors  are  used  the  sparking 
at  the  contacts  may  be  reduced  by  transforming  to  a  higher  vol- 
tage, 1 : 2,  and  using  a  high-voltage  lamp  for  the  load. 

The  Wenner  Speed  Controller. — This  device  enables  motors 
of  5  kw.  and  under  to  be  controlled  by  an  electrically  driven 
tuning  fork  of  the  desired  frequency.  The  connections  are 
indicated  in  Fig.  254. 

When  the  extra  field  resistance  a  is  in  circuit,  the  field  current 
is  cut  down  and  the  motor  increases  in  speed,  while  if  a  is  short- 
circuited,  the  field  is  increased  and  the  speed  decreased.  The 
fundamental  idea  is  to  arrange  a  special  rotating  switch  and  a 
contact  controlled  by  the  tuning  fork,  so  that  when  the  motor 


INDUCTANCE  AND  CAPACITY 


433 


speed  rises,  the  resistance  a  will  be  short-circuited  for  a  greater 
percentage  of  the  time,  thus  increasing  the  average  strength  of 
the  field  and,  in  consequence,  bringing  the  speed  back  to  its 
original  value. 

The  contact  is  controlled  by  the  electrically  driven  fork  and 
is  so  arranged  that  it  is  closed  for  half  a  complete  period,  that  is, 
for  half  the  time.  Contact  2  is  a  slip  ring,  which  is  electrically 
connected  to  the  half-ring  3;  thus  its  circuit  is  also  made  for 
half  the  time.  As  contacts  1  and  3  are  in  series,  the  resistance 
a  is  short-circuited  only  when  both  contacts  1  and  3  are  made. 

In  the  normal  running  position,  switch  3  lags  90°  behind  switch 
1  in  time  phase.  Thus  the  resistance  a  is  short-circuited  one- 
fourth  of  the  time  and  is  in  circuit  three-fourths  of  the  time. 


FIG.  254. — Diagram  for  Wenner  speed  controller. 


If  the  motor  tends  to  run  too  fast,  it  gains  on  the  fork  in  time 
phase  and  the  short-circuit  around  a  is  closed  for  a  longer  time, 
thus  increasing  the  average  strength  of  the  motor  field.  This 
slows  down  the  machine.  On  the  other  hand,  if  the  motor  tends 
.to  run  too  slow,  the  resistances  is  short-circuited  for  a  shorter 
time,  the  average  strength  of  the  motor  field  is  decreased  and  the 
speed  comes  back  to  its  original  value.  The  resistance  b  is  used 
in  synchronizing,  and  should  be  about  three-fourths  of  the  re- 
sistance a.  The  machine  is  started  with  resistance  b  in  circuit. 
When  synchronism  is  indicated  by  the  lamps,  b  is  replaced  by  a. 
The  rotating  switches  4  and  5,  which  are  in  electrical  connection 
with  the  slip  ring  2,  are  so  set  that  when  the  motor  and  the  fork 
are  in  synchronism  the  lamps  are  of  equal  brilliancy.  If  the 
motor  tends  to  hunt,  it  will  be  shown  by  the  ammeter. 

28 


434 


ELECTRICAL  MEASUREMENTS 
THE  VIBRATION  GALVANOMETER 


In  1891  Max  Wien  suggested  that  it  was  possible  to  greatly 
increase  the  sensitivity  of  the  detectors  used  in  alternating-cur- 
rent measurements,  where  zero  methods  are  employed,  by  taking 
advantage  of  the  principle  of  resonance.  To  do  this,  the  moving 
member  of  the  detector  is  mechanically  tuned  so  that  its  natural 
period  is  the  same  as  that  of  the  alternating  electro-magnetic 
forces  which  cause  its  deflection.  The  idea  was  realized  by 


FIG.  255. — Vibration  galvanometer,  Leeds  and  Northrup  Co. 

Wien  in  his  "optical  telephone."  The  later  development  of 
this  instrument  into  the  vibration  galvanometer  has  been  due 
more  especially  to  Wien,  Rubens,  A.  Campbell,  Duddell  and 
Drysdale,  who  have  utilized  both  the  moving  needle  and  the 
moving  coil  principles.30 

The  instrument  is  read  by  the  mirror  and  scale  method  and 
the  optical  arrangement  should  be  such  that  when  no  current 
is  passing,  a  sharply  defined  image  may  be  seen  on  the  screen. 
When  the  bridge,  or  other  apparatus  to  which  the  galvanometer 


INDUCTANCE  AND  CAPACITY 


435 


is-  connected,  is  out  of  balance,  the  galvanometer  coil  will  be 
set  in  vibration  and  this  image  will  become  extended  into  a  band 
of  light. 


100.0  100.1  1DOL2  100.3  100.4  100.5  100.6  100.7  100.8.100.9  101.0  M.I  101.2  101.3 
Frequency-Cycles  per  Second 

FIG.  255A. — Showing  effect  of  tuning,  on  current  and  voltage  sensitivities 
of  a  vibration  galvanometer. 


90 
80 
70 

(. 

|=o 

I40 

J30 
20 
10 
n 

t 

\s/ 

^ 

^ 

^ 

^0 

"\ 

/ 

\ 

"<; 

/Maximuni 
'         Point 

Sensitivity 

V=2lr 

\ 

N 

/ 

^ 

i 

v 

Ni 

/ 

j 

/ 

/ 

/ 

~   295  String  9.5  cms. 

/ 

/ 

7 

20.000 


80,000         100,000 


40,000  60,000 

Total  Flux 

FIG.  2555. — Showing  effect  on  the  voltage  sensitivity  of  a  vibration  gal- 
vanometer when  the  flux  cut  by  the  coil  is  varied. 

The  instrument  shown  in  Fig.  255  is  a  D' Arson val  galva- 
nometer so  designed  that  the  coil  may  be  given  a  high  rate  of 
vibration.  The  small  sketch  at  the  side  shows  how  the  rate  may 
be  varied,  that  is,  how  the  instrument  may  be  tuned  to  the 
frequency  of  the  circuit.  A  flat  strip  suspension  is  used,  the 


436  ELECTRICAL  MEASUREMENTS 

effective  length  of  which  may  be  adjusted  by  turning  the  milled  - 
head,  A,  at  the  upper  end  of  the  vertical  screw,  thus  securing  a 
coarse  adjustment.     The  fine  adjustment  is  made  by  turning 
the  milled  head,  B,  which,  by  means  of  the  spring,  S,  controls 
the  tension  on  the  suspension. 

On  account  of  the  large  restoring  moment  which  must  be  em- 
ployed to  obtain  a  high  rate  of  vibration,  the  sensitivity  of  a 
vibration  galvanometer  for  direct  currents  is  very  small.  It  is 
only  when  the  period  of  the  galvanometer  and  that  of  the  cur- 
rent coincide  that  the  current  sensitivity  rises  to  a  high  value. 
This  is  well  illustrated  by  Fig.  255A .  From  the  figure  it  is  clear 
that  if  the  sensitivity  is  to  be  maintained,  the  frequency  of  the 
current  must  be  constant;  in  the  case  shown  a  change  of  0.2  per 
cent,  in  the  frequency  reduces  the  current  sensitivity  by  about 
70  per  cent. 

The  characteristic  of  responding  freely  to  only  one  frequency 
permits  many  measurements  to  be  made  with  non-sinusoidal 
currents,  provided  the  harmonics  are  not  so  pronounced  that  they 
"force'7  the  vibration  of  the  movable  system.  In  one  very  good 
commercial  form  of  vibration  galvanometer  the  sensitivity  for 
the  third  harmonic  is  only  ^,00  o>  and  for  the  fifth  harmonic  only 
M2>ooo  'of  that  for  the  fundamental.  This  selective  sensitivity 
is  one  reason  why,  within  the  range  where  they  are  both  effective, 
the  vibration  galvanometer  is  superior  to  the  telephone  as  a 
detector,  unless  the  telephone  is  tuned  to  the  frequency  of  the 
current. 

As  current  of  constant  frequency  is  essential,  it  is  not  always 
possible  to  use  commercial  electric  circuits  as  sources  of  power 
in  those  alternating-current  measurements  where  the  vibration 
galvanometer  is  employed. 

Current  Sensitivity.31 — The  relation  between  current  and 
deflection  for  the  vibration  galvanometer  is  obtained  by  solving 
equation  9,  page  25,  in  which  i  =  IN  sin  (Nco)t.  Nu  is  N2ir  times 
the  fundamental  frequency  of  the  current;  for  the  fundamental 
N  =  1,  for  the  third  harmonic  N  =  3,  etc. 

The  equation  according  to  which  the  vibration  takes  place  is 

p(~ + k + Tt>  =  €IN  sin  (Nu)t       (54) 


INDUCTANCE  AND  CAPACITY  437 

An  idea  of  the  magnitudes  of  the  constants  in  (54)  will  be  given 
by  data  applying  to  an  instrument  investigated  by  Wenner. 

C  =  1.4  X  105  c.g.s. 
r  =  5,700 
k  =  0.018 
P  =  0.015 

Resistance  =  30  ohms 
Resonating  frequency  =  100  cycles  per  second. 

The  vector  solution  of  (54)  is 

8fl  ==  (T-(Na)'P}+jkNU  (55) 

If  co0  is  2?r  times  the  frequency  of  the  vibrating  coil  of   the 
galvanometer, 


P[co02-  (Nu)*] 

The  maximum  sensitivity  will  be  obtained  when  the  instrument 
is  exactly  tuned  to  the  frequency  of  the  circuit  by  changing  r  or 
when  to0  =  w,  N  =  1.  When  tuned,  the  galvanometer  is  but 
little  affected  by  the  harmonics  in  the  current  wave.  For  ex- 
ample, the  deflection  due  to  the  fundamental  will  be 

*-w  (57) 

and  that  due  to  a  current  of  N  times  the  fundamental  frequency 
will  be,  as  kNu  is  then  negligibly  small, 


-  A:2] 

That  is,  for  the  same  value  of  the  current, 

0!  _  P4i  -  ff  1  ,„, 

TN=       "IT 

Using  the  data  given  above  for  a  particular  instrument, 
f\ 
j-  =  4,200  approximately; 

or  the  sensitivity  to  the  third  harmonic  is  less  than  M.ooo  that 
for  the  fundamental. 

The  resonance  range  of  a  vibration  galvanometer  is  an  arbi- 
trary measure  of  the  exactness  of  tuning  required  if  a  high  sensi- 


438  ELECTRICAL  MEASUREMENTS 

tivity  is  to  be  maintained,  and  is  defined  as  the  fractional  change 
in  the  frequency  of  the  current  which  will  reduce  the  sensitivity 
of  the  instrument  to  one-half  its  maximum  value.  It  is  highly 
desirable  if  the  galvanometer  is  to  be  used  for  general  laboratory 
purposes,  that  the  resonance  point  be  not  too  sharply  defined. 
That  is,  the  resonance  range  of  the  instrument  should  be  large, 
as  great  as  0.2  of  1  per  cent. 

To  express  the  resonance  range  in  terms  of  the  constants  of 
the  galvanometer: 
when  the  instrument  is  perfectly  tuned, 

_  CIi 

If  the  frequency  of  the  supply  is  slightly  raised,  that  is,  if  N  is 
made  a  little  greater  than  1,  the  deflection  becomes 

CI, 

VN  = 


In  determining  the  resonance  range  the  change  in  N  is  supposed 
to  be  such  that  ^  =  -^r  so 

IN        21 1 

-  N2)  =  P2co2[l  -  N2]2 


and  as  AT"  is  very  nearly  1, 

k\/3 

I  —  N2  =  — ~ — >  approximately. 

r  co 

Frequency  of  current  which  halves  the  maximum  amplitude 

N  =  —  — ^ —    —7. 7 —  —  =  1  +  tii 

Resonating  frequency 

where  Ri  is  the  resonance  range  for  current. 

approximately.  (59) 

ru 

Voltage  Sensitivity.31 — When  a  vibration  galvanometer  is  so 
used  that  the  voltage  sensitivity  is  important,  it  should  be  noted 
that  as  the  coil  vibrates  it  cuts  the  flux  in  the  air  gap  and  thus 
sets  up  a  back  e.m.f.  which  is  in  time  quadrature  with  the  de- 
flection and  has  a  component  in  opposition  to  and  a  component 
in  quadrature  with  the  current. 

The  e.m.f.  which  is  effective  in  forcing  the  current  through  the 


INDUCTANCE  AND  CAPACITY  439 

circuit  is  the  vector  difference  of  the  applied  and  the  back 
e.m.fs. 
The  back  e.m.f.  is  given  by 


J  P[co02  -  co2]  +  jkw 
-  j/coC2P[coo2  -  co2] 


P2[co02  -  co2]2  +  /C2co2 

If  r  and  L  are  the  resistance  and  inductance  of  the  reactive  circuit 
in  which  the  galvanometer  is  inserted  and  V  is  the  applied  voltage, 

I(r  +  jcoL)  =  V  +  EB 
aid  '- 


••          rP[co02  -  co2]  -  fcco2L  +  ja[kr  +  LP(u>02  -  co2)  +  C2] 

In  this  case,  where  the  circuit  is  reactive,  the  sensitivity  is  not 
a  maximum  when  co0  =  co  but  when  T  is  so  adjusted  that 

P[».«  -  «']  =  -  2-  (62) 


Th3  corresponding  value  for  the  magnitude  of  0  is 


~ 


From  (62)  and  (62a)  it  is  seen  that  if  C  is  large  it  may  be  possible 
to  increase  the  deflection  by  placing  an  inductance  in  series  with 
the  galvanometer  and  slightly  raising  the  frequency  of  the 
supply,  for  the  fractional  increase  in  the  numerator  of  (62a)  may 
be  greater  than  that  in  the  denominator. 

To  obtain  the  greatest  possible  deflection  when  the  instrument 
is  used  in  a  circuit  of  fixed  inductance,  both  the  torsional  con- 
stant of  the  suspension,  T,  and  the  coil  constant,  C,  must  be 
adjusted.  C  may  be  varied  by  changing  the  strength  of  the  flux 
threading  the  coil.  When  both  T  and  C  are  adjusted,  the 
magnitude  of  6  is  a  maximum  when 


and 


co 


2L2 


C4=  [P2(coo2  -  co2) 


(63) 


440  ELECTRICAL  MEASUREMENTS 

The  corresponding  maximum  value  of  6,  obtained  by  63  and  61,  is  ' 

V 

2 

In  general  the  equivalent  impedance  of  the  circuit  including 
the  galvanometer  is 


r 


(f 


when  conditions  (63)  are  imposed,  this  reduces  to 

Z  =  2r  +  jo. 

Therefore,  when  the  deflection  has  been  made  a  maximum  by 
adjusting  both  r  and  C  the  current  is  in  phase  with  the  applied 
voltage  and 

'  =  1  ^ 

In  this  case  half  the  energy  supplied  to  the  instrument  is  ex- 
pended mechanically  and  half  in  electrical  heating. 

The  sensitivity  to  a  voltage  whose  frequency  is  N  times  the 
resonating  frequency  may  be  seen  from  (61).  If  the  voltage, 
VN,  is  applied  at  the  galvanometer  terminals, 

CV 
ON  =  prco2[  i  1  Nz]  approximately.  (66) 

By  a  process  similar  to  that  used  on  page  438  it  may  be  shown 
that  the  resonance  range  for  voltage,  Rv,  is 


Rv  =  +  Cg  approximatelv>  (67) 


It  may  be  possible  to  increase  the  voltage  sensitivity  of  the 
galvanometer  by  applying  the  potential  difference  through  a 
step-up  transformer  of  the  proper  ratio.  The  step-up  ratio, 
Ay  required  for  maximum  sensitivity  is  given  by 


where  r\  is  the  resistance  of  the  primary  and  r  that  of  the  galva- 

nometer circuit.     By  the  use  of  a  transformer  of  the  above  ratio 

^| 

the  voltage  sensitivity  is  increased  in  the  ratio  K-- 


INDUCTANCE  AND  CAPACITY  441 

References 

1.  ''Formulas  and  Tables  for  the  Calculation  of  Mutual  and  Self -Induc- 
tance"  (revised),  EDWARD  B.  ROSA  and  FREDERICK  W.  GROVER,  Bulletin 
of  the  Bureau  of  Standards,  vol.  8,  1912,  p.  1. 

2.  "On  a  Standard  of  Mutual  Inductance/'  ALBERT  CAMPBELL,  Proc. 
Royal  Society,  vol.  79,  1907,  p.  428.     Reprinted  in  "Collected  Researches  of 
the  National  Physical  Laboratory,"  vol.  4,  1908,  p.  215. 

3.  "A  Variable  Self  and  Mutual  Inductor,"  H.  B.  BROOKS  and  F.  C. 
WEAVER,  Scientific  Paper  No.  290,, Bureau  of  Standards.     "On  the  Use  of 
Variable  Mutual  Inductances,"  ALBERT  CAMPBELL,  Proc.  Physical  Society 
of  London,  vol.  21,  1907-09,  p.  69.     Reprinted  in  the  "Collected  Researches 
of  the  National  Physical  Laboratory,"  vol.  4,  1908,  p.  225. 

4.  "A  New  Determination  of  the  Ratio  of  the  Electromagnetic  to  the  Elec- 
trostatic Unit  of  Electricity,"  E.  B.  ROSA  and  N.  E.  DORSET,  Bulletin  of 
the  Bureau  of  Standards,  vol.  3,  1907,  p.  433. 

5.  "  Normal-Luftkondensatoren  und  ihre  absolute  Messung,"  E.  GIEBE, 
Zeit.  fur  Instrumentenkunde,  vol.  29,  1909,  p.  269. 

6.  "Ein    Satz    Normpl-Luftkondensatoren    mit  definierter  Schaltungs- 
kapazitat,"  H.  SHERING  and  R.  SCHMIDT,  Zeit.  fur  Instrumentenkunde,  vol. 
32,  1912,  p.  253. 

7.  "Fessenden    Wireless    Telegraph  Patents,"   The  Electrician,  vol.  55, 
1905,  p.  795.     "The  High-pressure  Electric  Condenser,"  Communication, 
F.  JERVIS-SMITH,  The  Electrician,  vol.  55,  1905,  p.  912.     Communication 
concerning  the  history  of  compressed  gas  condensers,  R.  A.  FESSENDEN. 
The  Electrician,  vol.   56,    1905-06,   p.    112.     "Ueber  die   Dampfung  von 
Kondensatorschwingungen,  III,  Leidener  Flaschen  und  Pressgas  Konden- 
satoren,"  MAX  WIEN,  Annalen  der  Physik,  vol.  29,  1909,  p.  679. 

8.  "Mica  Condensers  as  Standards  of  Capacity,"  HARVEY  L.  CURTIS, 
Bulletin  of  the  Bureau  of  Standards,  vol.  6,  1909-10,    p.  431. 

"The  Capacity  of  Mica  Condensers,"  ANTHONY  ZELENY,  Physical  Review, 
vol.  22,  1906,  p.  65. 

9.  "The  Capacity  and  Phase  Difference  of  Paraffined  Paper  Condensers 
as  Functions  of  Temperature  and  Frequency,"  FREDERICK  W.  GROVER, 
Bulletin  of  the  Bureau  of  Standards,  vol.  7,  1911,  p.  495. 

10.  "On  the  Measurement  of  Small  Capacities  and  Inductances,"  J.  A. 
FLEMING  and  W.  C.  CLINTON.     Proc.  Physical  Society  of  London,  vol.  18, 
1901-03,  p.  386. 

11.  For  a  discussion  of  the  application  of  both  Thomson's  and  Gott's 
methods  to  submarine  work,  see  "Capacity  Measurements  of  Long  Sub- 
marine Cables,"  J.  ELTON  YOUNG,  The  Electrician,  vol.  43,  1899,  p.  45. 

12.  "Notes  on    the  Use  of   the  Saunders  Capacity  Key  in  Comparing 
Capacities,"  ALEX.  MUIRHEAD,  The  Electrician,  vol.  25,  1890,  p.  487. 

13.  "The   Absolute   Measurement   of   Inductance,"   EDWARD   B.   ROSA 
and  FREDERICK  W.  GROVER,  Bulletin  of  the  Bureau  of  Standards,  vol.  1, 
1904-05,  p.  125. 


442  ELECTRICAL  MEASUREMENTS 

"  The  Absolute  Measurement  of  Capacity,"  EDWARD  B.  ROSA  and 
FREDERICK  W.  GROVER,  Bulletin  Bureau  of  Standards,  vol.  1,  1904-05, 
P.  153. 

14.  "On  the  Use  of  the  Secohmmeter  for  the  Measurement  of  Combined 
Resistances  and  Capacities,"  S.  R.  MILNER,  Phil  Mag.,  vol.  12,  1906,  p.  297. 

15.  "Messung  der  Inductionsconstanten  mit  dem  optischen  Telephon," 
MAX  WIEN,  Wied.  Annalen,  vol.  44,  1891,  p.  689. 

16.  "  Simultaneous  Measurement  of  the  Capacity  and  Power  Factor  of 
Condensers,"  FREDERIC  W.  GROVER,  Bulletin  of  the  Bureau  of  Standards, 
vol.  3,  1907,  p.  371. 

17.  "On  the  Loss  of  Energy  in  the  Dielectric  of  Condensers  and  Cables," 
BRUNO  MONASCH,  The  Electrician,  vol.  59,  1907,  pp.  416,  460,  504. 

18.  "On  the  Power  Factor  and  Conductivity  of  Dielectrics  when  Tested 
with  Alternating  Currents  of  Telephonic   Frequency  at  Various   Temper- 
atures," J.  A.  FLEMING  and  G.  B.  DYKE,  Journal  Institution  of  Electrical 
Engineers,  vol.  49,  1912,  p.  323. 

19.  "Zur  Messung  Dielektrischer  Verluste  mit  der  Wechselstrombriicke," 
KARL  WILLY  WAGNER,  Elektrotechnische  Zeit.,  vol.  32,  1911,  p.  1001. 

20.  "Messung  Unduktiver  Widerstande  mit  hochfrequenten  Wechsel- 
stromen.     Methode  zur  Messung  kleiner  Selbstinducktionskoeffizienten," 
E.  GIEBE,  Annalen  der  Physik,  vol.  24,  1907,  p.  941. 

21.  "On  Coefficients  of  Induction,"  A.  ANDERSON,  Phil.  Mag.,  vol.  31, 
1891,  p.  329. 

"Measurement  of  Inductance  by  Anderson's  Method  Using  Alternating 
Currents  and  a  Vibration  Galvanometer,"  E.  B.  ROSA  and  F.  W  GROVER, 
Bulletin  Bureau  of  Standards,  vol.  1,  1904-05,  p.  291. 

22.  "On  the  Application  of  Alternating  Currents  to  the  Calibration  of 
Capacity  Boxes,"  W.  STROUDE  and  J.  H.  OATES,  Phil.  Mag.,  vol.  6,  1903, 
p.  707. 

23.  Important  contributions  to  this  discussion  are:  "Professor  Hughes 
and  Self-induction;  Critical   Remarks  on  the  Discoveries  of  Mr.  Hughes 
Regarding  Self-induction  in  Metallic  Conductors,"  H.  F.  WEBER,  Electrical 
Review  (London),  vol.  18,  1886,  p.  321.     "Remarks  on  the  Second  Paper  of 
Mr.  Hughes,  Regarding  Self-induction,"  Electrical  Review  (London),  vol. 
19,  1886,  p.  30.     Notes  on  Electricity  and  Magnetism  II.     "The  Self-induc- 
tion and   Resistance   of   Compound  Conductors,"   LORD  RAYLEIGH,  Phil. 
Mag.,  vol.  22,  1886,  p.  469.     "On  the  Use  of  the  Bridge  as  an  Induction 
Balance,"  OLIVER  HEAVISIDE,  The  Electrician,  vol.  16, 1885-86,  p.  489. 

24.  "On  the  Use  of  Mutual  Inductometers,"  ALBERT  CAMPBELL,  Proc. 
Physical  Society  of  London,  vol.  22,  1909-10,  p.  207.     Also  The  Electrician, 
vol.  60, 1907-08,  p.  641.     Reprinted  in  "  Collected  Researches  of  the  National 
Physical  Laboratory,"  vol.  7,  1911,  p.  193.  "Inductance  Measurements," 
A.  CAMPBELL,  The  Electrician,  vol.  60,  1907-08,  p.  626. 

25.  "A  Method  for  the  Measurement  of  Self-induction,"  ERNEST  WILSON 
and  W.  H.  WILSON,  The  Electrician,  vol.  56,  1905-06,  p.  464. 

26.  "tlber  die  Bestimmumg  von  Inductionscoefficienten  mit  dem  Tele- 
phon," ADOLF  HEYDWEILLER,  Annalen  der  Physik,  vol.  53,  1894,  p.  499. 


INDUCTANCE  AND  CAPACITY  443 

27.  "The  Dead  Points  of  a  Galvanometer  Needle  for  Transient  Currents," 
ALEXANDER  RUSSELL,  Proc.  Physical  Society  of  London,  vol.  20,  1905-07, 
p.  235. 

28.  "On  a  Sine  Wave  Electrical  Oscillator  of  the  Organ  Pipe  Type," 
F.  K.  VREELAND,  Physical  Review,  vol.  27,  1908,  p.  286. 

29.  "Ein  Empfindlicher  Tourenregler  fur  Elektromotoren,"  E.  GIEBE, 
Zeit.  fur  Instrumentenkunde,  vol.   29,  1909,   p.   205.     London  Electrician, 
vol.  64,  1909-10,  p.  509. 

30.  "Das   Telephon  als  optischer   Apparat  zur   Strommessung,"    MAX 
WIEN,  Annalen  der  Physik,  vol.  42,  1891,  p.  593;  vol.  44,  1891,  p.  681. 
"Messung  der  Inductionsconstanten  mit  dem  optische  Telephon,"   MAX 
WIEN,  Annalen  der  Physik,  vol.  44, 1891,  p.  689.     "  Vibrationsgalvanometer," 
H.  RUBENS,  Annalen  der  Physik,  vol.  56,  1895,  p.  27.     "Ueber  die  Erzeugung 
und   Messung  von   Sinustromen.  Part  C.      Mess-instrumente  fur  schnelle 
Sinusstrome,"    MAX  WIEN.     Annalen  der  Physik,   vol.    4,    1901,   p.   439. 
"Note  on  the  Vibration  Galvanometer,"  ROY  P.  WELLS,  Physical  Review, 
vol.  23,  1906,  p.  504.     "On  the  Measurement  of  Mutual  Inductance  by 
Aid  of  the  Vibration  Galvanometer,"  A.  CAMPBELL,  Electrician,  vol.  60, 
1907-08,  p.  60;  Philosophical  Magazine,  vol.  14,  1907,  p.  494.     "A  Magnetic 
Shunt    Vibration    Galvanometer,"    HENRY    TINSLEY,   London   Electrician, 
vol.   69,    1912,   p.   939.     "Characteristics  and  Applications  of  Vibration 
Galvanometers,"  FRANK  WENNER,  Transactions  of  the  American  Institute 
of  Electrical  Engineers,  vol.  31,  1912,  p.  1243.      "On  a  Bifilar  Vibration 
Galvanometer,"  W.  DUDDELL,  Proceedings  of  the  Physical  Society  of  London, 
vol.  21,  1907-08,  p.  774. 

31.  "Theoretical    and    Experimental    Study    of    the    Vibration   Galva- 
nometer," FRANK  WENNER,  Bulletin  of  the  Bureau  of  Standards,  vol.  6, 
1909-10,  p.  347.     "  The  Maximum  Sensibility  of  a  Duddell  Vibration  Galva- 
nometer," H.  F.  Haworth,  Proceedings  of  Physical  Society  of  London,  vol. 
24,  1912,  p.  230.     "On  the  Vibration  Galvanometer  and  Its  Application  to 
Inductance  Bridges,"  S.  BUTTERWORTH,  Proceedings  of  the  Physical  Society 
of  London,  vol.  24,  1912,  p.  75. 


CHAPTER  VIII 


INDUCTION  INSTRUMENTS 

The  Induction  Principle. — In  1826  Arago  discovered  that  if  a 
copper  disc  be  rotated  about  a  vertical  axis  and  immediately 
below  a  magnetic  i  needle  which  is  pivoted  coaxially  with  the 
disc,  the  needle  is  deflected  in  the  direction  of  rotation  of  the  disc. 
If  the  speed  be  sufficiently  high  the  force  acting  on  the  needle  will 
overcome  the  earth's  directive  force  and  the  needle  will  be  set 

in  rotation.  The  inverse  experi- 
ment may  be  performed;  if  the 
magnet  be  rotated  on  its  pivot 
and  the  disc  be  free  to  move,  the 
disc  will  follow  the  magnet.  The 
correct  explanation  of  the  phenom- 
ena was  given  by  Faraday,  who 
showed  the  motion  to  be  due  to 
the  reaction  between  the  magnet 
and  the  currents  induced  in  the 
disc. 

In  this  inverse  experiment,  the 
phenomena   are  those   associated 
with    a   rotating   magnetic    field; 
that  is,   a  field   of    constant  in- 
tensity whose  angular  position  in 
FIG.  256.— Illustrating  Ferraris'  space  is  continually  changing.     In 
method  of  producing  a  rotating  1885  Ferraris  showed  that  a  rotat- 
magnetic  field.  .  .•    *  u         uii^-j 

ing  magnetic  field  could  be  obtained 

by  the  action  of  currents  in  suitably  placed  coils. 

Let  the  coils  be  arranged  as  in  Fig.  256,  and  consider  the 
magnetic  field  at  the  point  0.  At  any  instant  the  field  perpen- 
dicular to  the  plane  of  the  coil  A  at  this  point  is  given  by  hA  = 
kAiA  where  kA  is  a  constant  depending  upon  the  geometry  of  the 
coil,  and  iA  is  the  instantaneous  value  of  the  current.  If  sinu- 

444 


INDUCTION  INSTRUMENTS 


445 


soidal  currents  are  employed,  hA  =  kAIA  sin  ut.  The  field  due 
to  the  second  coil,  B,  will  be  hB  =  kBIB  sin  (co£  —  /8)  where  0 
is  the  time-phase  difference  of  the  two  currents.  If  the  coils  are 
of  equal  magnetic  strengths  (kAIA  =  kBIB)  and  are  placed  with 
their  planes  perpendicular,  and  if  the  two  currents  are  in  time 
quadrature  (j8  =  90°),  the  fields  at  any  instant  are  as  shown  in 
Fig.  257. 


A  sin  (at 


FIG.  257. — Showing  components  of  rotating  field. 
The  resultant  field  is 

H  =  \/k2APA  sin2  ut  +  kzAPA  cos2  coZ  =  kAIA,  a  constant. 

That  is,  the  field  at  0  i's  of  constant  intensity.  Its  direction 
at  any  instant  is  given  by  the  angle  y; 

sin  ut 

tan  y  =  -     —  =  tan  co£ 
cos  cot 

.'.  y   =   ut. 

The  resultant  field,  therefore,  rotates  with  a  constant  angular 
velocity,  co,  making  one  complete  rotation  in  the  time  required 
for  one  complete  cycle  of  the  current. 

If  a  copper  cylinder  be  suspended  by  a  thread  so  that  its  axis 


446 


ELECTRICAL  MEASUREMENTS 


is  vertical  and  includes  the  point  O,  the  rotating  field  will  cut  the 
cylinder,  induced  currents  will  be  set  up  and  the  cylinder  will 
rotate  just  as  does  the  disc  in  the  inverse  of  Arago's  experiment. 
This  was  one  of  Ferraris'  classic  experiments.  Ferraris,  however, 
did  not  appreciate  the  importance  his  discoveries  would  assume 
when  developed  along  engineering  lines,  for  he  states  that 
"  These  calculations  and  experimental  results  confirm  the  evident 
a  priori  conclusion  that  an  apparatus  founded  on  this  principle 
cannot  be  of  any  commercial  importance  as  a  motor,  and  while 
we  may  study  the  dimensions  in  order  to  increase  notably  its 
power  and  output,  it  would  be  useless  here  to  enter  upon  any 
consideration  of  this  problem.  Still,  the  experiments  described 
may  be  of  some  interest."1 

The  possible  application  of  the  principle  to  measuring  instru- 
ments was,  however,  mentioned  by  him. 

Application  to  Measuring  Instruments. — The  strength  of  the 
field  and  therefore  the  action  on  the  cylinder  will  be  greatly 


FIG.  258. — Magnetic  circuit  and  rotor  of  an  induction  instrument. 

increased  if  the  coils  be  provided  with  laminated  iron  cores. 
Fig.  258  shows  the  magnetic  circuit  of  an  induction-type,  watt- 
hour  meter  made  at  one  time  by  Siemens  and  Halske. 

In  the  figure,  A  A  is  a  laminated  ring  with  four  poles  FF,  EE 
projecting  toward  the  center  and  C  is  a  circular  laminated  iron 
core.  It  is  evident  that  the  poles  F  and  F  produce  a  field  whose 
general  direction  in  the  right-hand  diagram  is  horizontal,  while  the 
field  due  to  E  and  E  is  vertical.  The  strength  of  field  in  the  nar- 
row air  gap  will  be  considerable  and  in  this  field  is  placed  the 


INDUCTION  INSTRUMENTS  447 

hollow  aluminum  drum  B  which  forms  the  movable  element. 
The  similarity  of  this  arrangement  to  that  of  Ferraris  is  evident. 

The  general  explanation  of  the  action  of  induction  ammeters, 
voltmeters,  watt-meters  and  watt-hour  meters  may  be  based 
on  a  consideration  of  the  properties  of  rotating  magnetic  fields.* 
In  this  text,  however,  the  motion  of  the  rotor,  or  movable 
member,  will  be  considered  to  be  due  to  the  reciprocal  action  of 
one  pair  of  poles  on  the  currents  induced  by  the  other  pair  of 
poles. 

Referring  to  Fig.  258,  the  fields  due  to  coils  FF  induce  currents 
in  the  cylindrical  aluminum  rotor.  These  induced  currents  will 
tend  to  flow  in  closed  paths  perpendicular  to  the  axis  of  the  coil. 


FIG.  259. — Time-phase  diagram  for  induction  instrument. 

The  various  current  filaments  will  lag  behind  the  induced  e.m.fs. 
by  angles  dependent  on  the  resistances  and  inductances  of  the 
current  paths  in  the  cylinder.  Call  7  their  equivalent  phase  dis- 
placement. These  currents  are  in  a  position  to  be  deflected  by 
the  fields  set  up  by  coils  EE.  Similarly  the  currents  induced 
by  the  flux  from  EE  will  be  acted  upon  by  the  flux  from  FF. 
Assuming  sinusoidal  currents,  the  time-phase  relations  of  the 
various  quantities  are  shown  in  Fig.  259.  Let  the  fluxes  set  up 
by  FF  and  EE  be  $1  and  <J>2  respectively. 

The  angles  fii  and  @2  are  measured  from  an  arbitrary  zero  line. 
The  time-phase  difference  between  the  two  fluxes,  $1  and  3>2, 
is  02  --  0i.  EI  is  the  o.m.f.  induced  in  the  cylindrical  or  disc 
rotor  by  the  flux  $1  and  Ez  is  that  due  to  3>2.  EI  sets  up  induced 

*  Such  an  explanation  is  given  in  SOLOMON,  "Electricity  Meters," 
p.  111. 


448  ELECTRICAL  MEASUREMENTS 

currents  in  the  rotor,  which  on  account  of  the  inductances  of  the 
eddy-current  paths  lag  behind  E\.  The  equivalent  value  of 
these  currents  is  /i,  which  lags  behind  EI  by  the  angle  7.  Like- 
wise, the  equivalent  current  /2  lags  behind  E2.  The  turning 
moment  is  due  to  the  reaction  between  $1  and  72  less  that  between 
3>2  and  /i.  The  fluxes  and  currents  are  Assumed  to  be  sine  func- 
tions of  the  time.  The  instantaneous  torque  will  be  of  the  form 


and  the  average  torque  will  be 

*T 
1      =    --  (jl\.£l<Z>2    —    l\1<>d)l)    Ul 


cos  (7  +  90°  +  0i  -  02)  -  K'3>J2 

cos  (7  +  90°  +  /32  -  00 

-  X'$2/i  sin  (7  -  (02  -  00)  +  #'$1/2  sin  (7  +  (02  -  00). 
At  any  given  frequency  the  induced  currents  are 


and 

T        K&f 
=  ~Z~ 

where  Z  is  the  impedance  of  the  eddy-current  paths. 
Therefore, 


T  =  {   -  sin  (7  --  (02  -  00)  +   sin  (7  +   (02  -   00} 

K'"f$^$<> 

-^4  cos?  gin  (02  -  00.  (1) 

The  accelerating  torque  is  proportional  to  the  product  of  the 
two  fluxes,  to  the  sine  of  the  time-phase  angle  between  them, 
and  to  the  frequency. 

If  the  armature  is  in  motion,  there  will  be  a  retarding  effect 
due  to  its  movement  through  the  two  alternating  fields.  This 
retarding  effect  will  be  proportional  to  the  mean  square  values  of 
the  fields  and  to  the  angular  velocity  of  the  armature  a/,  or  to 


[^f)i^  $9^T 

-Y+  2  I"'' 


INDUCTION  INSTRUMENTS 


449 


By  proper  design  this  term  is  kept  as  small  as  possible  in  watt- 
hour  meters,  and  the  armature  is  seldom  allowed  to  make  more 
than  one  revolution  per  second. 

Induction  Ammeters  and  Voltmeters.— As  an  illustration  of 
the  application  of  these  principles  to  measuring  instruments,  the 
Westinghouse  induction  ammeters  and  voltmeters  may  be 
taken.2-3  Fig.  260A  shows  the  electrical  and  magnetic  circuits 
of  the  ammeter.  The  line  current  enters  by  the  terminals  TT  and 
flows  through  the  coil  P,  giving  rise  to  the  flux,  3>P,  which  crosses 
the  air  gap  in  the  horizontal  direction.  The  magnetic  circuit 
carries  a  second  winding,  S,  which  with  the  coils  AA'  forms  a 
closed  circuit. 


FIG.  260. — Westinghouse  induction  ammeter. 

The  current  induced  in  this  secondary  circuit  sets  up  a  flux, 
$s,  which  crosses  the  air  gap  in  the  vertical  direction.  The  two 
fluxes  are  in  the  proper  space  relation  to  produce  a  torque  on 
the  thin  aluminum  cup  which  forms  the  movable  element.  They 
must  also  have  the  proper  time-phase  relation.  This  is  attained 
by  the  transformer  action  of  the  two  windings,  P  and  S. 

Referring  to  the  vector  diagram  accompanying  Fig.  260 A,  the 
flux  3>p  links  both  P  and  S.  It  is  therefore  the  mutual  flu;x  and 
induces  in  the  winding  S  an  e.m.f.,  Es,  which  lags  90°.  The 
flux,  $s,  threads  the  secondary  winding,  S,  but  not  the  primary 
winding,  P,  consequently  it  is  the  secondary  leakage  flux;  it  will 

29 


450 


ELECTRICAL  MEASUREMENTS 


be  in  time  phase  with  Is,  the  current  which  flows  in  S.  The 
induced  voltage,  E8,  must  overcome  the  reactance  drop  due  to 
$s  and  the  ohmic  drop  in  S.  The  fluxes  $P  and  $s  differ  in  time 
phase,  being  somewhat  more  than  90°  apart,  and  will  produce  a 
torque  on  the  movable  element. 


FIG.  260A. — Electric  and  magnetic  circuits  of  Westinghouse  induction 

ammeter. 

I  is  the  line  current  and  as  the  arrangement  is  a  sort  of  current 
transformer, 

$>s  =  K2I 

KJ 


These  values  inserted  in  (1)  give  for  the  torque, 


INDUCTION  INSTRUMENTS  451 

T  =  KJ*  -p  [sin  (02  -  00]  (2) 

02  —  ^  =  90°  approx. 

The  torque  and  therefore  the  deflection  are  proportional  to  the 
mean  square  of  the  line  current. 

Frequency  and  Temperature  Effects  in  Westinghouse  Ammeter. 
—In  order  that  an  instrument  may  be  of  the  highest  utility,  its 
indications  must  be  free  from  the  effects  of  change  of  frequency 
and  of  temperature.  Practically,  these  effects  must  be  reduced 
to  amounts  which  are  consistent  with  good  engineering  practice, 
since  they  cannot  be  made  zero.  As  Z,  7,  and  (02  —  00  vary 

cos  7  sin  (02  —  00 

with  the  frequency,  the  factor  -  — ^—          -  can  be  made 

& 

only  approximately  constant.  By  careful  design,  the  maximum 
difference  in  the  readings  corresponding  to  a  definite  current, 
for  any  two  frequencies  between  25  and  60  cycles,  may  be  reduced 
to  about  0.5  per  cent. 

In  order  that  the  temperature  effect  be  nil,  for  any  definite 

current,    S^P  cos  7  must  be  constant  with  respect  to  temperature. 
LI 

This  relation  is  readily  attained  as  the  arrangement  is  electrically 
equivalent  to  a  current  transformer.  It  is  to  be  remembered 
that  in  a  current  transformer  if  the  primary  current  be  kept 
constant,  the  secondary  current  will  be  practically  unaffected 
by  considerable  changes  in  the  resistance  of  the  secondary  circuit. 
This  means  that  the  mutual  flux,  $P,  increases  in  proportion  to 
the  secondary  resistance.  The  flux  $s  is  due  to  the  secondary 
current  and  is,  therefore,  fixed  in  value;  consequently,  if  by  the 

'use  of  the  proper  materials  in  the  secondary,  $P  be  given  a  tem- 

17 

perature  coefficient  equal  to  that  of -,  the  required  adjust- 
ment is  attained.  Therefore,  the  secondary  circuit  is  made 
partly  of  copper  and  partly  of  resistance  wire  of  low  temperature 
coefficient,  the  proper  proportion  of  the  two  being  determined 
experimentally,  so  that  allowance  can  also  be  made  for  the 
temperature  coefficient  of  the  iron  and  of  the  controlling  spring. 
In  the  voltmeter  the  primary  coil  is  wound  with  fine  wire,  and 
an  external  non-inductive  resistance  wound  with  wire  of  zero 
temperature  coefficient  is  used.  The  proportion  of  ohmic  re- 


452 


ELECTRICAL  MEASUREMENTS 


Resistor  and  Reactor 


sistance  to  total  impedance  is  made  very  high,  so  that  the  current 

in  the  primary  coil  is  practically  independent  of  the  frequency. 
The  Induction  Wattmeter.  —  The  induction  principle  is  used 

in  switchboard  wattmeters. 

Fig.  261  shows,  in  diagram,  the  magnetic  and  electric  circuits  of 

a  switchboard  instrument  made  by  the  Westinghouse  Company. 
The  core  is  built  up  of  thin  stampings.     The  voltage  coil,  in 

series  with  a  reactor,  is  connected  across  the  circuit;  it  magnet- 

izes the  core  as  indicated  by  the 
arrows.  This  potential  coil  flux 
crosses  the  air  gap  in  the  horizontal 
direction.  The  current  coils  give  rise 
to  the  flux  in  the  vertical  direction. 
These  two  fluxes  are,  therefore,  in 
the  appropriate  space  relation  for 
producing  a  torque  on  the  thin 
aluminum  cylinder  which  is  pivoted 
in  the  air  gap. 

As  the  air  gaps  are  large,  the  fluxes 
will  be  proportional  to  the  currents. 
Consequently  at  a  fixed  frequency, 


/     \     / 


Voltage 


Current 


wvwv- 

>  ^2          Cl 


l  sin  (ft  - 


T  = 


As  before,  /32  —  /3i  is  the  time-phase 

difference  of  the  fluxes. 

The  time-phase  diagram  is  given  in 

FIG.  261.— Electric  and  mag-  Fig.  262. 

netic  circuits  of  Westinghouse       The  potential  circuit  of  an  indue- 

tion  wattmeter  is  purposely   made 

highly  inductive  so  that  $1  naturally  lags  75°  or  80°  behind  the 
applied  voltage;  it  will  not  lag  90°  on  account  of  the  energy  losses 
in  the  iron  cores  and  in  the  windings. 

The  angle  a  is  the  amount  by  which  $1  falls  short  of  being  in 
quadrature  with  V. 

a  +  032  -  £1)  +  0  =  90°, 

_ 

so  the  torque  is  given  by 

P("\o   'y 

T=  KbVI  ~  |~  sin  (90  -  a  -  6)  =  KbVI  —*-  cos  (a  +  6). 


INDUCTION  INSTRUMENTS 


453 


The  power  is  VI  cos  0.  If  a  =  0,  that  is,  if  the  useful  potential- 
coil  flux  is  adjusted  so  that  it  is  exactly  90°  out  of  time  phase  with 
the  applied  voltage,  the  torque  will  be  proportional  to  the  power 
in  the  circuit.  This,  of  course,  is  the  proper  adjustment  and 
must  be  attained  by  the  addition  of  special  phase  shifting  or 
lagging  devices  by  which  the  useful  potential-coil  flux  in  the  air 
gap  is  brought  into  quadrature  with  the  line  voltage. 

If  the  useful  flux  lags  behind  the  applied  voltage  by  less  than 
90°,  that  is,  if  a  is  + ,  the  wattmeter  is  said  to  be  under-lagged ; 
if  a.  =  0,  it  is  exactly  lagged  and  if  a  is  — ,  that  is,  if  the  flux  has 
been  caused  to  lag  more  than  90°,  the  instrument  is  over-lagged. 

V  Applied  to  Load 


and  Potential  Coil 
Lag  Angle  of  Load 


Practically  iii  Phase 
with  Load  Current  / 


Unlagged,  Practically  in  Phase 
with   / Pt  Current  in  Potential  Coil 


FIG.  262. — Time-phase  diagram  for  induction  wattmeter. 

The  construction  of  the  magnetic  circuit  of  the  potential  coil 
should  be  such  that  the  useful  potential-coil  flux  is  naturally 
nearly  90°  out  of  phase  with  the  applied  voltage;  the  required 
amount  of  additional  lagging  is  thus  reduced.  The  less  the  re- 
liance placed  on  the  lagging  device  the  better  will  the  instrument 
behave  when  it  is  subjected  to  wide  variation  of  frequency  and 
to  distorted  wave  form. 

In  the  instrument  shown  in  Fig.  261  the  desired  quadrature 
relation  of  the  applied  voltage  and  the  useful  potential-coil  flux 
is  obtained  by  use  of  a  second  winding,  S,  the  circuit  of  which 
may  be  closed  through  the  resistance  R^ 

It  will  be  seen  that  this  lagging  arrangement  is  a  sort  of 
transformer  with  a  large  primary  leakage  flux,  much  of  which  is 
in  the  series  reactor.  There  is  considerable  resistance  in  the 


454 


ELECTRICAL  MEASUREMENTS 


potential-coil  circuit  so  that  when  the  circuit  of  R2  is  open  the 
instrument  is  under  lagged,  that  is,  the  angle  between  the  ap- 
plied voltage  and  the  useful  potential-coil  flux  is  less  than  90°. 
Referring  to  the  diagram,  Fig.  263,  (in  which  a  1/1  ratio  is 
assumed),  the  flux  which  threads  the  voltage  winding  and  the 
secondary  winding,  S,  (shown  in  Fig.  261)  is  the  mutual  flux 
$M.  This  flux  is  also  the  useful  potential-coil  flux;  it  crosses 
the  air  gap  in  the  horizontal  direction  and  cuts  the  hollow 
aluminum  cylinder  which  is  pivoted  in  the  gap.  This  cylinder 
forms  the  rotor  or  movable  member  of  the  wattmeter.  <J>M 
induces  an  e.m.f.,  E,  in  both  the  voltage  and  the  secondary 
windings.  The  applied  voltage,  V,  must  overcome  the  voltage, 
E,  induced  by  $M,  the  ohmic  drop  in  the  primary  circuit  IiRi, 
and  the  reactive  drop  in  the  primary  circuit,  IiX\,  due  to  the 


Secondary  Open 


V'          Secondary  Closed 
FIG.  263. 


primary  leakage  flux.  As  indicated  in  Fig.  263 A,  the  angle  A 
between  the  applied  voltage,  V,  und  the  useful  potential-coil 
flux,  $M,  is  less  than  90°. 

When  the  secondary  circuit  is  closed  through  the  resistance, 
R2,  (see  Fig.  2635)  a  current,  72,  flows  in  it.  The  total  pri- 
mary current,  7i,  is  the  vector  sum  of  —  72  and  the  no  load 
current  70.  It  is  seen  that  closing  the  secondary  circuit  rotates 
1 1  counter-clockwise  so  that  when  I\X\  and  I\R\.  are  added  to 
—  E  the  vector,  V,  which  represents  the  applied  voltage,  is  also 
rotated  counter-clockwise  and  the  angle  A  between  the  applied 
voltage,  Vj  and  the  useful  flux,  $M,  is  increased. 

In  order  to  adjust  the  lagging  so  that  A  is  90°  it  is  necessary 
to  calibrate  the  instrument  with  a  load  of  unity  power  factor, 
and  then  to  calibrate  it  with  a  load  of  low  power  factor,  about 
0.5.  If  the  two  results  do  not  agree,  the  resistance  R2  (Fig.  261) 


INDUCTION  INSTRUMENTS 


455 


must  be  altered  and  another  trial  made,  and  so  on  until  the 
results  do  agree. 

As  the  correct  action  of  an  induction  wattmeter  depends  on 
having  the  angle  A  exactly  90°,  it  is  obvious  that  a  change  of 
frequency,  with  its  accompanying  change  of  reactance  of  the 
potential  coil,  will  introduce  errors.  An  induction  wattmeter 
which  is  adjusted  for  use  on  a  60-cycle  circuit  will  be  in  error  if 
used  at  25  cycles.  As  the  correctness  of  the  instrument  is  de- 
pendent on  the  frequency,  it  will  be  affected  by  changes  of  wave 
form.  See  the  discussion  of  the  induction  watt-hour  meter,  page 
473. 

In  another  lagging  arrangement,  not  commonly  used  in 
America,  the  potential  coil  is  shunted  by  a  non-inductive  resis- 


FIG.  264.  —  Diagram  for  lagging  arrangement  for  induction  wattmeter. 

tance  and  this  divided  circuit  placed  in  series  with  a  reactance. 
This  whole  combination  forms  the  potential  circuit  of  the 
instrument. 

This  arrangement  is  indicated  in  Fig.  264. 

The  equations  are: 


IA     = 


BC, 


By  altering  the  non-inductive  resistance,  R,  the  component, 
IR,  may  be  varied  and  the  phase  of  IP)  or  more  correctly,  the  phase 
of  <£p,  which  will  differ  a  little  from  that  of  IP,  may  be  changed 
until  A  =  90°. 

In  the  induction  wattmeter,  temperature  changes  affect  the 
resistance  of  the  rotor  or  movable  element;  the  induced  currents 
are  thus  cut  down  about  0.4  per  cent,  per  degree  of  temperature 


456  ELECTRICAL  MEASUREMENTS 

rise.  Consequently,  unless  there  is  some  special  compensation 
for  temperature  effects,  this  form  of  wattmeter  has  a  large  tem- 
perature coefficient.  In  the  Westinghouse  instrument  shown  on 
page  452  the  compensation  is  made,  as  in  the  ammeter,  by  ad- 
justing the  temperature  coefficient  of  the  circuit  containing  Rz. 

For  the  discussion  of  the  induction  watt-hour  meter,  see  the 
chapter  on  "Electricity  Meters,"  page  457. 

The  advantages  claimed  for  the  induction  type  of  instrument 
for  switchboard  work,  are: 

1.  Extremely  long  scales,  due  to  the  fact  that  the  movable 
element  can  turn  through  nearly  360°. 

2.  Compactness;  this  reduces  the  size  of  the  switchboard  panel. 

3.  Errors  due  to  external  fields  of  the  fundamental  frequency 
are  small. 

4.  Robust  construction,  which  facilitates  repairs. 

5.  The  ratio  of  torque  to  weight  of  moving  element  is  large. 
There  are  also  certain  disadvantages,  some  of  which  may  be 

overcome  by  careful  design. 

1.  The  indications  are  affected  by  changes  of  frequency  and 
wave  form;  these  errors  are  very  important  in  induction  watt- 
hour  meters,  especially  at  low  power  factors. 

2.  There  are  temperature   errors  caused   by  changes  in  the 
resistance  of  the  armature  due  both  to  changes  of  room  tem- 
perature and  to  self-heating  in  the  instrument. 

3.  The  torque  always  increases  with  the  load  on  the  instrument, 
so  in  cases  of  sudden  overload  the  pointer  may  be  thrown  violently 
against  the  stop  and  either  bent  or  displaced. 

4.  Alternating  currents  must  be  used  in  checking  the  instru- 
ments,  this    is    sometimes    inconvenient    when    dealing    with 
portable  instruments. 

References 

1.  "Electrodynamic    Rotation    Produced   by    Alternate    Currents,"    G. 
FERRARIS,  The  Electrician,  vol.  36,  1895-96,  p.  281.     (Paper  was  read  March 
18,  1888.) 

2.  (<A   New    Form  of  Induction  Ammeter  or  Voltmeter,"  PAUL  MAO 
GAHAN,  Electric  Journal,  vol.  4,  1907,  p.  113. 

3.  "Induction   Type    Indicating    Instruments,"    P.    MACGAHAN,    Trans 
American  Institute  Electrical  Engineers,  vol.  31,  part  II,  1912,  p.  1565. 

4.  "Electricity  Meters,"  H.  G.  SOLOMON,   1906,  Charles  Griffin  &  Co., 
London. 


CHAPTER  IX 
ELECTRICITY  METERS 

Watt-hour  Meter. — In  connection  with  the  supply  of  elec- 
trical energy  for  lighting  and  power,  it  is  necessary  to  have  some 
form  of  integrating  meter;  that  is,  a  meter  which  will  give, 
not  the  rate  at  which  energy  is  supplied  to  the  circuit,  but  the 

total  amount  of  energy  supplied  during  a  given  time,  as  for  in- 

/•*, 
stance,  a  month.     Such  a  meter  must  evaluate   I    vidt;  v  and    i 

Jh 

are  the  instantaneous  values  of  the  voltage  and  current;  the 
time  during  which  the  energy  is  supplied  is  t2  —  t\.  It  is  custom- 
ary to  express  this  time  in  hours.  The  energy  is  then  stated  in 
watt-hours,  or,  more  frequently,  in  kilowatt-hours. 

The  necessity  for  accurately  measuring  electrical  energy  is 
apparent  from  the  fact  that  in  the  United  States,  alone,  the 
charges  for  the  electrical  energy  furnished  for  light  and  power 
were,  for  the  year  1916,  approximately  $450,000,000. 

The  essentials  of  the  watt-hour  meter  will  be  better  appreciated 
if  one  approved  form  of  the  instrument  be  described.  The 
Thomson  watt-hour  meter  for  direct  currents  will  be  selected, 
for  this  was  the  first  successful  commutating  meter.  It  was 
placed  on  the  market  in  the  latter  part  of  1889,  has  passed 
through  the  usual  processes  of  development,  and  is  still  regarded 
as  one  of  the  best  of  its  class. 

The  instrument  consists  of  a  small  motor  which  is  provided 
with  a  magnetic  brake.  The  motor  drives  a  counter  whose  indi- 
cations on  a  system  of  dials  are  proportional  to  the  total  number 
of  revolutions  which  have  been  executed  by  the  armature. 

No  iron  is  used  in  either  the  field  or  the  armature  of  the  motor, 
therefore  all  magnetic  effects  are  directly  proportional  to  the 
currents. 

The  fields  of  the  motor  are  placed  in  the  main  circuit  in  series 
with  the  load.  The  armature,  in  series  with  a  suitable  resistance, 
is  connected  across  the  supply  mains.  The  driving  torque  of  the 

457 


458 


ELECTRICAL  MEASUREMENTS 


motor  is  proportional  to  VI  and  the  retarding  torque  clue  to  the 
brake  is  proportional  to  the  angular  velocity  of  the  disc.  Broadly 
speaking,  therefore,  the  energy  supplied  to  the  circuit  during  a 
given  time  will  be  proportional  to  the  number  of  revolutions  of 
the  armature  during  that  time;  in  other  words,  to  the  reading 
on  the  dials  of  the  counter. 

Referring  to  Fig.  265,  the  main  current  passes  .through  two 
similar  field  coils  of  low  resistance  F.  In  a  two-wire  meter  these 
coils  are  connected  in  series.  The  potential  circuit,  which  con- 
tains the  armature^.,  is  connected  on  the  line  side  of* the  main 


FIG.  265. — Thomson  watt-hour  meter  for  direct  currents. 

coils.  The  armature  (now  made  in  a  spherical  form  to  reduce 
the  weight)  is  carried  by  an  upright  spindle  which  at  its  upper 
end  gears  by  means  of  a  worm  into  the  very  light  train  of  wheels 
which  moves  the  pointers  of  the  counter  over  the  dials.  The 
current  is  carried  to  the  armature  through  silver-tipped  brushes 
'  which  rest  with  a  very  slight  pressure  on  a  silver  commutator  of 
small  diameter.  The  brushes  are  adjusted  before  the  meter 
leaves  the  factory  and  should  be  very  carefully  handled. 

In  the  early  designs  of  this  meter,  the  series  resistance,  R,  was 
wound  non-inductively  on  cards  and  carried  in  an  envelope  at 
the  back  of  the  instrument.  It  is  now  combined  with  the  light- 
load  coil,  F',  mentioned  below.  In  a  110- volt  instrument,  the 
total  resistance  of  the  potential  circuit  is  about  2,500  ohms. 


ELECTRICITY  METERS.  459 

The  lower  end  of  the  shaft  is  provided  with  a  removable  steel 
pivot  which  rests  in  a  sapphire  or  diamond  jewel  carried  by  a 
spring  support  in  the  end  of  the  jewel  screw  (see  Fig.  267).  This 
screw  can  be  turned  back  so  that  the  disc  D  is  clamped  against 
the  magnets  M;  the  pivot  is  thus  relieved  of  all  strain  during 
transportation. 

The  brake  disc,  D,  now  made  of  aluminum,  moves  through  the 
fields  of  the  permanent  magnets,  M.  To  change  the  retarding 
torque  and  therefore  the  speed  of  the  meter,  the  distance  of  the 
poles  of  the  magnets  from  the  axis  of  the  disc  may  be  altered. 

In  order  to  compensate  at  light  loads  for  the  effects  of  mechan- 
ical friction,  a  field  coil  of  fine  wire,  F',  is  connected  in  series  with 
the  armature.  A  small  permanent  driving  torque  is  thus  ob- 
tained. By  adjusting  the  position  of  the  coil  with  respect  to  the 
armature  this  torque  may  be  made  such  that  the  registration  at 
light  loads  is  commercially  correct;  at  the  same  time  the  load  cur- 
rent necessary  to  start  the  meter  is  much  reduced.  The  effect 
of  the  light-load  coil  at  the  higher  loads  is  insignificant. 

To  show  that  the  number  of  revolutions  during  a  given  time  is 
practically  proportional  to  the  energy  supplied  to  the  load  via 
the  meter, 

Let  V  =  line  voltage. 
7  =  line  current. 

Ia  =  current  in  potential  circuit  or  armature. 
R  =  resistance  of  potential  circuit. 
o)  =  angular  velocity  of  armature. 
h  =  field  due  to  drag  magnets. 
r  =  resistance  to  eddy  currents  in  brake  disc. 
KS  =  driving  torque  due  to  light-load  coil. 
KM  =  initial  friction  torque. 

K  and  /c,  with  various  subscripts,  are  constants  or  proportion- 
ality factors. 

The  flux  through  the  armature  due  to  the  main  coils,  F,  will  be 
proportional  to  I  and  that  due  to  the  starting  or  light-load  coil,  F', 
will  be  proportional  to  la,  so 

total  flux  through  armature  =  kFI  +  kfla. 
The  back  e.m.f.  in  the  armature  circuit  will  be  proportional  to 
the  product  of  the  flux  and  the  angular  velocity. 
Back  e.m.f.  =  k(k?I  -f-  kF>Ia)u 


460  ELECTRICAL  MEASUREMENTS 

The  armature  current  will  be 


V  -  kkrla        V  - 
Ia  =  -^  =        --  ~  Approximately. 


The  driving  torque  due  to  the  main  coils  may  be  represented 
by  KFIIa  and  that  due  to  the  light-load  coils  by  KF>Ia2.  As  the 
meter  is  operated  at  a  constant  voltage  and  the  torque  due  to  the 
light-load  coil  is  small,  it  is  allowable  to  consider  this  quantity 
as  constant;  it  will  be  denoted  by  Ks.  The  total  accelerating 
torque  is 

/KF\  (KFkkF\ 

\R)  VI  "  I~B  -)*<*  +  KB 

The  total  retarding  torque  is  that  due  to  the  mechanical  fric- 
tion of  the  meter  (including  windage)  plus  that  due  to  the  mag- 
netic brake.  The  friction  torque  has  a  certain  initial  value, 
denoted  by  KMj  and  increases  more  rapidly  than  the  speed;  its 
Value  may  then  be  represented  by  KM  +  KM'^.  The  brake  torque 
is  proportional  to  the  angular  velocity  of  the  disc  and  if  the  tem- 
perature of  the  disc  and  the  magnets  is  constant,  may  be  expressed 

,      kDh2u 

by  -*~  =  KDu.  (2) 

Consequently  the  total  retarding  torque  is 

KM  +  KDu  +  KM,rf  (3) 

For  steady  motion  the  accelerating  and  retarding  torques  must 
be  equal.  Equating  (1)  and  (3)  gives  for  the  angular  velocity  of 
the  disc, 

co  =  KiVI  -  K2I2u  +  K's  -  K'M  -  KfM'<**  (4) 


The  terms  on  the  right-hand  side  of  the  equation  which  involve 
co  are  small  corrections  due  to  the  back  e.m.f.  and  the  change  of 
friction  torque  with  the  speed. 

It  is  seen  that  if  the  light-load  coil  is  adjusted  so  that  at  no- 
load  the  meter  is  just  on  the  point  of  starting  (K1  '  M  very  slightly 
greater  than  K's),  the  angular  velocity  of  the  armature  will  be 
practically  proportional  to  the  power  supplied  to  the  load;  and 
it  at  once  follows  that  the  total  number  of  revolutions,  N,  exe- 
cuted by  the  armature  in  a  given  time  is  proportional  to  the 
energy  supplied  to  the  load  during  that  time. 


ELECTRICITY  METERS  461 

For  meters  as  actually  constructed 

watt-hours  registered  on  dials  =  KhN.  (5) 

This  is  fundamental  and  applies  to  all  watt-hour  meters. 
The  factor  Kh  is  called  the  watt-hour  constant,  and  is  the 
number  of  watt-hours  of  energy  necessary  to  cause  one  revolution 
of  the  movable  system. 

General  Discussion  of  Essential  Characteristics. — A  considera- 
tion of  the  uses  to  which  the  watt-hour  meter  is  put  will  show 
that  the  instrument  should  possess  certain  characteristics. 

In  order  that  the  first  cost  and  the  expense  of  maintenance 
may  not  be  too  great,  electricity  meters  must  be  simple  in 
design  and  must  contain  no  parts  which  are  subject  to  rapid 
deterioration. 

It  is  desirable  that  the  reading  in  kilowatt-hours  be  given 
directly  by  the  dials,  especially  in  small  meters;  this  avoids  the 
necessity  for  multiplying  the  dial  readings  by  a  constant.  A 
possible  source  of  misunderstanding  between  the  consumer  and 
the  supply  company  is  thus  avoided. 

The  meter  should  be  protected  by  a  case  which  can  be  sealed 
and  which  is  dust,  water  and  insect  proof;  the  arrangement 
should  be  such  that  there  is  little  likelihood  that  a  short-cir- 
cuit can  occur  during  the  removal  and  the  replacement  of  the 
meter  cover.  It  is  desirable  that  the  electrical  connections  to 
the  meter  be  so  made  that  it  is  not  possible  to  tamper  with  the 
instrument;  in  certain  cases  special  devices  are  used  for  covering 
all  the  connections  from  the  service  wires  to  the  meter  so  that 
it  is  impossible  for  the  customer  to  draw  current  which  does  not 
pass  through  the  meter. 

Permanency  of  calibration  is  a  prime  requisite.  On  a  large 
system  it  is  not  practicable  to  test  and  adjust  the  majority  pf 
the  meters  oftener  than  once  a  year.  Consequently,  they  must 
maintain  their  accuracy  for  at  least  this  period.  In  the  case  of 
large  consumers  where  the  amount  of  money  involved  is  consider- 
able the  inspections  are  more  frequent. 

To  attain  permanence  of  calibration  the  friction  at  the  pivots 
and  commutator  and  the  retarding  torque  of  tjie  magnetic  brake 
must  remain  constant.  It  is  essential" that  the  commutator  and 
brushes  be  capable  of  operating  continuously  for  long  periods 
without  undue  increase  of  friction  and  without  attention.  To 


462 


ELECTRICAL  MEASUREMENTS 


secure  this  result^  Elihu  Thomson,  after  experimenting  with  many 
materials,  was  led  by  a  knowledge  of  the  mechanical  and  elec- 
trical properties  of  silver,  and  experience  with  contacts  made  of 
it,  to  adopt  the  pure  metal  for  both  the  commutator  and  the 
brushes.  This  solved  the  greatest  problem  in  the  design  of 
commutating  meters. 

The  magnets  used  in  connection  with  the  retarding  disc  or 
brake  must  retain  their  strength.  This  involves  the  choice  of 
a  proper  magnet  steel,  a  correct  design  (a  nearly  closed  magnetic 
circuit)  and  the  artificial  ageing  of  the  magnets  by  partial  de- 
magnetization and  by  the  proper  heat  treatment  at  moderate 
temperatures.  From  equation  (2)  in  the  demonstration  already 


Normal  distribution. 


Distribution  after  a  short  circuit. 


FIG.  266. — Showing  effect  of  a  short-circuit  on  the  distribution  of  magnet- 
ism in  the  drag  magnets  of  a  direct-current  watt-hour  meter. 

given  (page  460),  it  will  be  seen  that  a  1  per  cent,  change  in  the 
strength  of  the  retarding  magnets  affects  the  accuracy  of  the 
meter  by  2  per  cent. 

The  magnets  should  be  so  placed  that  their  strength  is  not 
likely  to  be  altered  by  the  field  due  to  the  current  coil. 

Besides  the  natural  deterioration  of  the  magnets  there  is  the 
chance  of  an  accidental  change  due  to  short-circuits,  and  the 
magnets  should  be  so  arranged  that  this  effect  will  be  minimized. 
The  enormous  and  sudden  rush  of  current  through  the  current 
coils  during  a  short-circuit  sets  up  a  magnetic  field  which  may  be 
strong  enough  to  change  entirely  the  distribution  of  magnetism 
in  the  drag  magnets  and  cause  the  meter  to  over-register.  Such 
a  change  in  the  distribution  of  magnetism  is  illustrated  in  Fig.  266. 

The  field  coils  must  be  firmly  held  and  kept  apart  by  spacing 


ELECTRICITY  METERS 


463 


blocks  so  that  they  cannot  alter  their  positions  or  draw  together 
and  crush  the  armature  if  a  short-circuit  occurs. 

As  friction  losses  in  the  instrument  are  unavoidable,  they  must 
be  reduced  to  a  minimum  and  must  remain  practically  constant 
over  long  periods  of  time.  Therefore  the  moving  parts  should 
be  light,  the  jewels  and  pivots  of  the  best,  and  kept  in  good  order. 
The  jewels  should  be  carried  by  spring  supports  as  this  construc- 
tion increases  the  life  of  the  jewel  by  the  elimination  of  "  hammer- 
ing" and  consequently  assists  in  maintaining  accuracy  at  light 
loads. 


<-Shaft 


Steel  Ball 

— -^ 

Clamping  Nut 


FIG.  267. — Jewel  supports  for  watt-hour  meters. 

Cupped  diamond  jewels  are  now  used  in  direct-current  meters 
of  large  capacity;  this  contributes  materially  to  the  maintenance 
of  accuracy  at  light  loads. 

In  order  to  reduce  the  wear  on  the  moving  parts  of  a  meter, 
the  full-load  speed  is  limited  to  about  50  revolutions  per  minute. 

The  commutator  should  be  of  small  diameter  and  smooth 
and  must  be  kept  free  from  oil  and  dust  of  all  kinds;  the  brushes 
must  be  smooth  and  the  brush  pressure  properly  adjusted. 

The  counter  should  have  the  minimum  possible  friction  and 
the  worm  and  wheel  connection  to  the  armature  spindle  should 
be  properly  adjusted.  Steady  pins  should  be  used  to  insure 
permanence  of  the  adjustment. 

The  torque  of  the  meter  should  be  high  so  that  the  unavoidable 
irregularities  in  friction  may  not  cause  inaccuracies,  for  in  time 
the  pivot  and  jewel  as  well  as  the  commutator  become  rough,  es- 
pecially if  the  meter  be  subject  to  vibration  and  sudden  jars. 


464  ELECTRICAL  MEASUREMENTS 

i 

The  commutator  is  very  likely  to  be  troublesome,  especially  if 
any  sparking  occurs  due  to  the  presence  of  dust  or  oil. 

The  fact  that  a  meter  has  a  high  torque  is  advantageous  only 
when  it  is  associated  with  a  light  moving  element.  The  ratio 

Full-load  torque 
Full-load  speed  X  friction 

should  be  large  if  the  accuracy   of  the  meter  is   to  be   only 
slightly  affected  by  the  wear  of  the  jewel,  pivot  and  commutator. 

Of  late  years  the  weight  of  the  movable  element  has  been 
much  decreased  by  the  use  of  a  spherical  self-supporting  armature 
and  an  aluminum  brake  disc. 

The  effect  of  changes  of  room  temperature  on  the  accuracy 
of  the  meter  should  be  reduced  to  a  minimum.  It  is  evident 
that  the  net  effect  of  temperature  on  the  resistance  of  the  disc 
and  on  the  drag  magnets  should  be  balanced  by  the  change  in 
the  resistance  of  the  armature  circuit.  The  average  temperature 
coefficient  of  the  meter  between  20°  and  40° C.  should  not  be 
more  than  0.2  per  cent,  per  degree  at  either  10  per  cent  or  100 
per  cent  of  full-load  current.  Tests  show8  that  the  temperature 
coefficients  of  representative  direct-current  watt-hour  meters  of 
American  manufacture  vary  between  +0.26  a.nd  +0.07  per 
cent  per  degree  C.,  most  of  them  being  about  +0.1  per  cent. 

As  the  armature  circuit  carries  considerable  current  and  i 
in  part  made  of  copper,  its  resistance  (R  in  formula  1)  wil 
rise  and  decrease  the  driving  torque  when  the  meter  is  firs 
connected  in  circuit;  consequently,  tests  should  not  be  mad< 
until  the  permanent  state  of  temperature  has  been  reached 
which  may  require  about  20  minutes. 

When  a  load  is  thrown  on  the  meter,  the  heat  liberated  in 
the  current  coils  also  raises  the  temperature  of  the  copper- 
wound  armature  and  increases  the  resistance  of  the  potentia 
circuit,  thus  decreasing  the  registration.8  This  effect  increases 
with  the  load  current  and,  up  to  the  time  of  attainment  of  tern 
perature  equilibrium,  with  the  length  of  time  the  current  is  left  on 

From  equation  (2)  it  will  be  seen  that  the  effect  of  the  self 
heating  of  the  meter  on  the  magnetic  brake  is  to  decrease  the  re- 
tarding torque  and  cause  the  meter  to  speed  up.  However,  as 


ELECTRICITY  METERS 


465 


'the  brake  is  at  a  considerable  distance  from  both  the  current  and 
potential  coils,  the  error  is  practically  that  due  to  the  change  in 
temperature  of  the  potential  circuit. 

The  net  result  of  the  heating  due  to  the  current  coils  is  that  if 
the  meter  is  adjusted  at  full-load  by  changing  the  position  of  the 
drag  magnets  and  then  at  light  load  by  means  of  the  light-load 
coil,  the  registration  will  be  correct  at  light  and  at  full-load, 
will  be  a  little  too  great  at  intermediate  loads  and  a  little  too 
small  at  overloads,  the  general  form  of  the  percent-registration 
curve  being  that  shown  at  AHF  in  Fig.  268. 


1.020 

D_ 

^1.000 

£ 

MO  990 

A^ 

... 

—  — 

h 

G 

^^^ 

^^ 

•^  £• 

V   A    QOA 

~^~' 

-^.^ 

F 

*3 

0 

40  60  80  100 

Per  Cent  Full  Jioad 


120 


140 


100 


FIG.  268. — Pertaining  to  self-heating  error  due  to  current  coils  of  direct- 
current  watt-hour  meter. 


In  detail,  if  there  were  no  errors  due  to  the  heat  from  the  cur- 
rent coils  the  per  cent-registration  curve,  if  the  meter  were  adjusted 
to  register  correctly  at" full-load  and  at  light  load,  would  be  that 
derived  from  equation  (4),  all  the  coefficients  being  constant. 
If  the  adjustments  were  made  at  10  per  cent  load  and  full-load, 
the  curve  would, be  AHB. 

The  effect  of  the  heating  is  to  increase  R.  This  causes  the 
upper  parts  of  the  curve  to  droop,  the  result  being  the  curve  AC. 
By  moving  the  drag  magnets  the  curve  AC  may  be  shifted  bodily 
so  that  it  takes  the  position  DGE  and  by  means  of  the  light-load 
coil  the  registration  at  some  low  load  (TO  per  cent  load)  may  be 
made  correct.  The  percent-registration  curve  is  then  AHF. 
The  registration  is  correct  at  10  per  cent  load  and  at  full-load. 
These  self-heating  errors  are  important  in  portable  rotating 
standard  watt-hour  meters  such  as  are  referred  to  on  page  495. 

The   meter  should   be  unaffected   by  local   magnetic   fields. 

30 


466 


ELECTRICAL  MEASUREMENTS 


Trouble  may  be  experienced  from  improper  wiring,  leads  carry- 
ing large  currents  being  placed  too  near  the  meter.  This  would 
be  likely  to  occur  in  heavy  direct-current  switchboard  work, 
for  in  this  case  the  meter  coils  consist  of  only  a  few  turns  and  the 
busbars  at  the  back  of  the  switchboard  may  be  very  near  the 
meter.  To  obviate  this  trouble  a  special  astatic  wattmeter  has 
been  designed.  It  is  shown  diagrammatically  in  Fig.  268A. 


FIG.  2QSA. — Diagram  for  astatic  watt-hour  meter. 


The  spindle  carries  two  equal  armatures,  one  operating  in  the 
field  above  and  the  other  in  the  field  below  a  straight  conductor. 
In  consequence  of  this  arrangement,  variations  of  the  local  field, 
which  affect  its  strength  equally  at  the  upper  and  lower  armatures, 
have  no  effect  on  the  registration.  The  drag  magnets  are  so 
placed  that  if  the  strength  of  one  is  increased  by  the  extraneous 
field,  that  of  the  other  is  diminished.  The  whole  retarding 
device  is  enclosed  in  an  iron  shield. 

Any  watt-hour  meter  should  maintain  its  accuracy  under 
varying  conditions  of  voltage  and  load.  In  general,  in  the  neigh- 
borhood of  the  station,  the  voltage  on  a  system  of  electrical 
supply  will  remain  nearly  constant,  especially  if  the  system  be 
large;  but  at  a  distance,  owing  to  insufficient  copper  in  the' con- 
ductors, the  voltage  variations  may  be  considerable  and  the 
accuracy  of  the  meter  should  not  be  affected  by  them.  Because 
of  heating,  the  resistance  of  the  potential  circuit  of  the  meter  is 
dependent  on  the  line  voltage.  Consequently,  a  change  in  line 


ELECTRICITY  METERS 


467 


voltage  does  not  produce  a  proportionate  change,  in  the  speed  of 
the  armature.  At  moderate  and  full  loads  an  increase  of  voltage 
will  tend  to  make  the  meter  register  too  little.  At  light  loads, 
where  the  light-load  coil  F'  furnishes  a  considerable  part  of  the 
driving  torque,  an  increase  of  voltage  tends  to  make  the  meter 
register  too  high,  for  the  torque  of  the  light-load  coil,  which  in- 
creases as  the  square  of  the  current  in  the  armature  circuit,  may 
more  than  counterbalance  the  tendency  of  the  meter  to  register 
too  low  due  to  the  increase  in  the  resistance  of  the  potential 
circuit.  Practically,  the  effect  of  voltage  variations  will  depend 
on  the  load  on  the  meter,  for  the  position  of  the  drag  magnets 


1.040 


1.020 
£  a  1.010 
M' 5"  1.000 


.970 


A  =  Commutator  Meter 
B  =  Mercury  Meter 


80 


100 
Per  Cent  Normal  Voltage 


110 


120 


FIG.  269. — Showing  effect  of  voltage  variation  on  the  registration  of  direct- 
current  watt-hour  meters  at  full-load  current. 

and  of  the  light-load  coil  is  adjusted  at  some  standard  voltage. 
For  direct-current  meters,  at  full-load  current,  a  variation  of  from 
10  per  cent  above  to  10  per  cent  below  the  normal  voltage  should 
not  affect  the  accuracy  by  more  than  3  per  cent  and  at  10  per 
cent  of  the  rated  full-load  current,  the  effect  should  not  be  more 
than  5  per  cent. 

Accuracy  at  light  loads  is  of  great  importance,  for  it  is  seldom  that 
the  meter  in  an  installation  is  worked  at  full  capacity.  Indeed, 
for  a  great  portion  of  the  time  the  load  on  the  meter  may  be  but  a 
small  fraction  of  its  rated  capacity,  and  under  these  conditions  it 
is  essential  that  the  energy  be  measured  as  accurately  as  possible. 

The    meter  should    rotate  continuously  with  2   per  cent  of 


468 


ELECTRICAL  MEASUREMENTS 


rated  full-load  current,  and  at  10  per  cent  of  rated  full-load  cur- 
rent should  register  correctly  to  within  3  per  cent.  The  light- 
load  adjustment  must  be  such  that  the  meter  does  not  " creep," 
that  is,  rotate  continuously  when  the  consumer  is  not  using 
energy.  This  should  be  true  even  when  the  supply  voltage  is  10 
per  cent  higher  than  that  at  which  the  meter  was  adjusted. 
Electrical  supply  companies  which  give  careful  attention  to  their 
meters,  instruct  testers  to  leave  them  so  adjusted  that  they  regis- 
ter correctly  to  within  1  per  cent  at  from  5  to  10  per  cent  of  full- 
load  and  to  within  1  per  cent  at  full-load. 

The  periodic  service  tests  on  a  large  distribution  system  where 
careful  attention  is  given  to  the  upkeep  of  the  meters  may  be 
expected  to  show  results  comparable  with  the  following: 


Com  mutating  meters 

Light  load, 
5  to  10  per 
cent,  of 
full-load 

Full- 
load 

Per  cent  of  total  number  of  meters  which  register  between  98  and  102 
per  cent  of  the  correct  value 

60  0 

90  5 

Per  cent  of  total  number  of  meters  which  register  between  95  and  105 
per  cent  of  the  correct  value                     ... 

91   9 

98  3 

Per  cent  of  total  number  of  meters  which  register  between  90  and  110 
per  cent  of  the  correct  value     

98  3 

98  9 

Induction  meters 

Per  cent  of  total  number  of  meters  which  register  between  98  and  102 

84  0 

93  8 

Per  cent  of  total  number  of  meters  which  register  between  95  and  105 

97  7 

98   6 

Per  cent  of  total  number  of  meters  which  register  between  90  and  110 
per  cent  of  the  correct  value 

98  6 

98  8 

The  tests  were  made  at  intervals  of  from  six  months  to  a  year. 

The  aim  of  careful  supply  companies  is  to  so  maintain  their 
meters  that  a  full-load  accuracy  of  98  per  cent  or  better  is 
obtained. 

The  energy  losses  in  the  meter  must  be  small,  for  the  potential 
coil  of  the  instrument  is  in  circuit  continuously,  even  though  the 
consumer  is  using  no  energy.  The  expense  of  energizing  the 
potential  coils  falls  on  the  supply  company;  in  the  aggregate  it 
may  be  a  considerable  item. 


ELECTRICITY  METERS. 


469 


When  the  consumer  uses  energy  the  voltage  at  the  load  is 
diminished  by  the  IR  drop  in  the  current  coils  of  the  meter.  This 
of  course  varies  with  the  load.  For  a  small  direct-current  meter 
(5  amp.)  the  drop  in  the  field  coils  may  be  about  1  per  cent  of  the 
line  voltage  when  the  rated  full-load  current  is  used.  The  ex- 
pense of  energizing  the  field  coils  falls  on  the  consumer. 

Use  of  Watt-hour  Meters  on  Three -wire  Circuits. — For  meter- 
ing on  low-tension,  three-wire,  direct-current  circuits  such  as  are 
used  in  congested  districts  in  cities,  two  ordinary  two-wire  meters 
may  be  used,  one  with  the  current  coils  in  the  positive  lead,  the 
potential  circuit  being  connected  between  this  lead  and  the  neu- 
tral wire,  while  the  other  is  similarly  connected  on  the  negative 


Supply 


Load 


Neutral 

FIG.  270. — Diagram  for  three-wire  direct-current  watt-hour  meter. 

side  of  the  circuit.  Such  an  arrangement  is  free  from  errors  due 
to  the  unbalancing  of  the  voltage  of  the  circuit  and  to  unequal 
currents  in  the  positive  and  negative  leads;  it  is,  therefore,  a 
desirable  arrangement  when  the  circumstances  are  such  that  these 
effects  may  become  very  large. 

Ordinarily,  a  single  three-wire  meter  is  employed.  In  this 
instrument,  one  of  the  current  coils  is  in  the  positive,  while  the 
other  is  in  the  negative  lead. 

When  traversed  by  equal  currents,  the  two  current  coils  should 
have  equal  effects  on  the  armature.  The  potential  circuit  may 
be  connected  between  the  positive  or  the  negative  lead  and  the 
neutral  or  between  the  positive  and  negative  leads.  Fig.  270 
shows  diagrammatically  a  three-wire  meter  with  the  first  con- 
nection. 


470  ELECTRICAL  MEASUREMENTS 

Theoretically,  the  three-  wire  meter  is  subject  to  certain  errors; 
for  instance,  with  the  connection  shown  in  Fig.  270  the  potential 
lead  being  on  main  No.  1,  an  error  will  occur  if  the  voltages  are 
unbalanced,  for  the  power  given  to  the  circuit  is 

P  =  VJ,  +  F2/2. 

The  angular  velocity  of  the  armature  is  supposed  to  be  propor- 
tional to  this  quantity,  while  in  reality  it  is  proportional  to 

Fi(/i  +  /*). 

Therefore,  with  a  steady  load,  the  correction  which  must  be 
added  to  the  reading,  reduced  to  watts,  to  obtain  the  true  power, 
is 

C  =  72(F2  -  70- 

This  correction  will  be  positive  or  negative  depending  on  whether 
Vz  or  Vi  is  the  larger.  With  the  potential  lead  connected  to 
main  No.  2, 

C  =  !,(¥,  -  y2). 

If  the  potential  circuit  is  connected  between  the  positive  and 
negative  mains,  the  angular  velocity  of  the  disc  will  be  propor- 
tional to 


where  V  is  the  potential  difference  between  the  positive  and  nega- 
tive mains.  The  correction  in  watts  which  must  be  added  to 
the  reading  to  obtain  the  true  power,  will  be  the  difference  be- 
tween P  and  this  quantity,  or 

c  =  (1  2  -  /Q(y«  -  yj 

2 

The  error  in  the  registration  will  be  zero  if  the  currents  in  the 
current  coils  are  equal,  even  though  the  voltages  are  unbalanced. 
It  will  also  be  zero  if  the  voltages  are  balanced,  even  though  the 
currents  flowing  in  the  two  current  coils  are  unequal.  If  the 
leads  to  the  meter  and  load  be  of  considerable  resistance  and  the 
voltages  are  balanced  before  any  current  is  drawn,  the  meter 
will  always  read  too  high  when  unequal  currents  are  taken  by 
the  two  sides  of  the  load;  for  if  /i  is  greater  than  72  the  quan- 
tity (F2  —  Vi)  is  positive  and  the  correction  negative.  If  7  1  is 
less  than  72,  (F2  —  Vi)  is  negative  and  again  the  correction  is 
negative. 


ELECTRICITY  METERS  471 

If  alternating  currents  are  used  and  the  loads  are  reactive, 
these  relations  are  still  further  complicated  by  the  phase  dis- 
placements of  the  currents.  The  corresponding  corrections  are 
readily  deduced. 

Practically  it  is  impossible  to  make  allowance  for  these  errors, 
for  the  loads  on  the  two  sides  of  the  installation  are  continually 
shifting;  the  best  that  can  be  done  is  to  see  that  the  load  distribu- 
tion is  such  that  the  two  sides  are  well  balanced. 

The  Use  of  Commutating  Watt -hour  Meters  on  Alternating- 
current  Circuits. — Before  the  introduction  of  induction  watt- 
hour  meters,  it  was  customary  to  employ  commutating  meters 
on  reactive  circuits.  In  this  case  the  reactance  of  the  potential- 
coil  circuit  introduces  an  error,  for  the  potential-coil  current  in 
it  is  not  in  time  phase  with  the  voltage  applied  to  the  load  and 
the  mean  product  of  the  currents  in  the  fixed  and  movable  ele- 
ments of  the  watt-hour  meter  will  not  be  proportional  to  the 
power  delivered  to  the  circuit.  The  error  so  arising  will  be  in- 
significant when  the  instrument  is  used  on  a  non-inductive  load, 
but  when  the  power  factor  is  low,  the  error  may  become  of  im- 
portance. A  general  discussion  of  this  phase-angle  error  will  be 
found  in  the  section  on  the  "  Electrodynamometer  Wattmeter," 
page  309. 

Lag  Coil. — It  is  necessary  to  adjust  the  phase  difference  be- 
tween the  current  in  the  armature  and  the  current  in  the  field 
coil  so  that  this  phase  difference  is  the  same  as  that  between  the 
voltage  applied  to  and  the  current  in  the  load,  and  to  do  this 
without  greatly  altering  the  current  in  the  field  coils.  This  is 
accomplished  by  the  use  of  the  "lag  coil,"  which  is  a  non-inductive 
shunt  placed  around  the  field  coils  of  the  instrument. 

Its  action  may  be  made  clear  by  the  following: 

Let  Rp  =  resistance  of  potential-coil  circuit. 
Lp  =  inductance  of  potential-coil  circuit. 
Re  =  resistance  of  current  coils. 
Lc  =  inductance  of  current  coils. 

RS  =  resistance  of  "lag  coil"  or  shunt  around  current  coils. 
7  =  load  current. 

Is  —  current  in  lag  coil. 

Ic  =  current  in  current  coil. 

IP  =  current  in  potential  coil. 

V  =  line  voltage. 


472 


ELECTRICAL  MEASUREMENTS 


P.D.s  =  potential  difference  at  terminals  of  current  and  lag  coils. 

dp  =  phase  displacement  of  potential-coil  current  with  respect  to  V. 
8c  =  phase  displacement  of  current  in  current  coils  with  respect  to 

line  current, 
w  =  2ir  times  frequency. 


PDS 


FIG.  271.  —  Diagrams  for  lag  coil  of  commutating  meter. 

On  account  of  the  reactance  of  the  field  coils,  the  current  Ic  in 
them  will  lag  behind  (PD)S  as  indicated.  The  vector  sum  of 
Is  and  Ic  is  the  total  or  load  current,  /.  By  adjusting  the  resist- 
ance Rs  the  current  in  the  field  coil  Ic  may  be  made  to  lag  behind 
the  main  current  I  by  an  angle  equal  to  the  lag  of  the  current  in 
the  potential  coil  behind  the  applied  voltage;  in  other  words,  6C 
may  be  made  equal  to  6P.  The  instrument  then  becomes 
practically  correct. 

Analytically,  for  the  potential  circuit, 


7     _  y 

y 


The  lag  of  this  current  behind  the  potential  will  be' 


For  the  shunted  current  coils 


=  PDS 


Ri 

Re.  -  i 


Ic  lags  behind  PDS  by  the  angle  \F  =  tan"1  -5-^- 

KC 

The  main  current  is 


•ELECTRICITY  METERS  473 

and  lags  behind  (PD)S  by  the  angle  "#' 

V  =  tan-1  ^~£r^r~ti~2  4-TcoL  V2 

LC& 

tan  0C  =  tan(^  —  ^  )  =  ^-— ; — 5^- 

/is  ~r  lie 

To  make  0C  =  8Pj 


_ 
RP       RS  -\~  RC 

The  proper  value  of  Rs  is  therefore 


Rs  =  (L  J  fl" " 


which  is  independent  of  the  frequency. 

The  Induction  Watt-hour  Meter. — It  has  been  shown  above 
that  commutating  watt-hour  meters  may  be  made  to  register 
correctly  on  circuits  of  all  power  factors.  Formerly,  lagged 
meters  of  this  class  were  in  common  use  on  alternating-current 
circuits;  they  have  now  been  superseded  by  induction  watt-hour 
meters  for  the  following  reasons.  The  moving  element  of  the 
induction  meter  may  be  made  very  light  and  at  the  same  time  the 
torque  may  be  kept  high.  This  reduces  the  wear  on  the  lower 
pivot  and  jewel  and  lessens  the  chance  of  errors  due  to  pivot 
friction.  There  is  no  commutator  to  become  rough  through  wear 
and  sparking,  thus  increasing  the  friction,  and  there  are  no  brushes 
to  keep  in  order.  The  net  result  is  a  great  decrease  in  the  first 
cost  of  the  meters  and  in  the  cost  of  maintaining  them,  a  decrease 
in  the  current  necessary  to  start  the  meters  and  an  increase  in  the 
accuracy  of  the  registration  at  light  loads  (see  page  468).  This 
last  point  is  of  the  utmost  importance.  The  losses  in  the  poten- 
tial coils  are  less  in  the  induction  than  in  the  commutating  meter 
and  as  the  loss  goes  on  continuously  24  hours  a  day,  this  fact  is 
of  importance. 

Fig.  272  shows  in  a  schematic  manner  the  essential  parts  of  an 
induction  watt-hour  meter.  The  explanation  of  the  creation  of  an 
accelerating  torque  in  this  instrument  is  the  same  as  that  given 
for  the  induction  wattmeter,  page  448.  The  accelerating  torque 
is  balanced  by  the  retarding  torque  of  a  magnetic  brake  as  in 
direct-current  meters. 


474 


ELECTRICAL  MEASUREMENTS 


The  terminals  T3  and  7%  are  connected  to  the  supply  while  the 
load  is  connected  between  TI  and  T2. 

PC  is  the  coil  of  the  highly  inductive  potential  circuit;  it  is 
connected  across  the  line.  Most  of  the  flux  through  this  coil 
passes  down  the  central  core  and  returns  via  BA  and  CE.  Some 
of  it,  however,  goes  to  the  potential  coil  lug  PL  and  thus  magnet- 
izes it.  The  flux  which  proceeds  outward  from  PL  cuts  the 
pivoted  disc  D  which  forms  the  movable  element  of  the  mjgter. 


FIG.  272.  —  Showing  electric  and  magnetic  circuits  of  induction  watt-hour 

meter. 

The  line  current  flows  through  the  oppositely  wound  series  coils 
FF.  '  On  the  passage  of  currents  in  all  the  coils,  the  flux  from 
PL  induces  currents  in  the  disc  which  are  acted  upon  by  the 
flux  due  to  F,  and  the  flux  from  FF  induces  currents  in  the  disc 
which  are  acted  on  by  the  flux  due  to  PL.  With  sinusoidal  cur- 
rents a  driving  torque  is  thus  generated  whose  value  is 


See  page  448. 


T  =  K'VI  sin  (02  -  ft)  -  fci  + 


The  retarding  torque  is  due  to  the  movement  of  the  disc  through 
the  air  gaps  of  the  drag  magnets,  which  in  this  meter  are  placed 
diametrically  opposite  PL. 

For  steady  motion  the  driving  torque  must  equal  the  retarding 


ELECTRICITY  METERS  475 

torque  of  the  brake,  or  KDu  ,  where  a/  is  the  angular  velocity  of 
the  disc.     The  term 


represents  the  drag  due  to  the  motion  of  the  disc  through  the 
alternating  fields  in  the  air  gaps.  It  will  vary  with  the  load  on 
the  meter,  and  be  a  source  of  error,  but  by  correct  design  this 
error  may  be  made  negligibly  small,  and  the  angular  velocity  of 
the  movable  element  becomes 


But  the  potential  circuit  is  highly  inductive,  so  (see  Fig.  262) 

«'  =  KVI  cos  (0  +  a)  (6) 

where  0  is  the  power  factor  angle  of  the  load  and  a  is  the  departure 
from  exact  time  quadrature  of  the  useful  potential-coil  flux  and 
the  potential  applied  to  the  load  (see  page  453). 

If  the  meter  is  properly  lagged,  that  is,  if  a  =  0,  the  angular 
velocity  of  the  disc  is  proportional  to  the  power  and  the  total 
number  of  revolutions  executed  in  any  time  interval  is  pro- 
portional to  the  kilowatt-hours  of  energy  supplied  during  that 
time. 

The  Lag  Adjustment.  —  Exact  time  quadrature  of  the  useful 
potential-coil  flux  and  the  voltage  applied  to  the  load  is  obtained 
by  the  use  of  a  lag  coil,  LC,  which  is  wound  about  the  potential- 
pole  tip.  The  circuit  of  this  coil  is  completed  by  the  resistance 
Rz  which  is  adjusted  until  the  desired  phase  relation  (A  =  90°) 
is  established.  A  simplified  diagram  of  the  potential  circuit 
is  shown  in  Fig.  272  A.  It  will  be  seen  that  the  arrangement  is 
equivalent  to  a  transformer  with  large  leakage  reactances. 
For  simplicity  a  1  :  1  ratio  is  assumed.  The  disc,  which  serves 
as  the  rotor,  projects  into  the  air  gap,  a2,  and  is  cut  by  the  total 
flux  in  the  gap,  <£2.  The  mutual  flux  which  cuts  the  primary 
and  secondary  is  <f>M  and  the  primary  and  secondary  leakage 
fluxes  are  <£Li  and  3>/,2,  respectively,  $Li  being  the  leakage  flux 
which  cuts  through  the  disc.  The  total  flux  through  the  primary 
is  $1.  When  the  secondary  is  open  the  angle  A  is  less  than  90° 
due  to  the  IR  drop  in  the  potential  coil.  When  the  secondary 


476 


ELECTRICAL  MEASUREMENTS 


is  closed  a  magnetomotive  force  proportional  to  and  in  phase  with 
/2  is  introduced.  The  leakage  flux  <J>L2  will  be  in  time  phase  with 
and  substantially  proportional  to  /2;  likewise  the  leakage  flux 
&LI  will  be  in  time  phase  and  substantially  proportional  to  I\. 
The  mutual  flux  <J>M  is  proportional  to  and  in  phase  with  I0,  Io 
being  the  vector  sum  of  /i  and  72  as  in  any  transformer.  <£>i  is 
the  vector  sum  of  $M  and.  $/,],  and  3>2  is  the  vector  sum  of  $M 
and  3>L2-  —Ely  the  induced  voltage  in  the  primary,  will  obviously 
be  90°  ahead  of  $1.  By  the  proper  adjustment  of  /2,  $Lz  may  be 


B 

Secondary  Closed 
FIG.  272  A.  —  Diagram  for  lag  adjustment  of  induction  watt-hour  meter. 

made  of  such  magnitude  that  $2,  the  total  flux  cutting  the  disc, 
is  swung  clockwise  so  that  angle  A  is  made  90°.  In  order  to  make 
the  adjustment,  one  must  have  at  command  a  source  of  sinu- 
soidal current  which  has  the  voltage  and  frequency  for  which  the 
meter  was  designed  and  from  which  loads  can  be  taken  at  unity 
power  factor  and  some  lower  power  factor,  0.5,  or  thereabouts. 
One  must  also  know  whether  the  power  factor  is  due  to  a  lagging 
or  a  leading  current. 

The  meter  is  set  up  and  adjusted  by  moving  the  drag  magnets 
so  that  it  registers  correctly  at  unity  power  factor.  If  the 
registration  is  correct  the  constant  K,  calculated  by  the  formula 

K        -Pi— 

' 


will  agree  with  that  stated  by  the  makers.  (P  is  the  power,  t  is 
the  time  in  seconds  required  for  N  revolutions.)  The  light-load 
adjustment  is  now  made. 


ELECTRICITY  METERS  477 

Keeping  these  adjustments  the  same,  the  meter  is  then  tested 
at  the  lower  power  factor.  If  it  is  correctly  lagged,  the  values 
of  K  from  the  two  tests  will  be  the  same.  Suppose,  however, 
that  the  constant  given  by  the  second  test  is  greater  than  that 
obtained  at  unity  power  factor.  This  shows  that  the  meter 
runs  too  slow  at  low  power  factors.  Therefore,  if  the  current 
lags,  see  equation  (6), 

cos  (0  -f  a)  <  cos  B 

e  +  a  >  e 

therefore  a  is  a  positive  angle  (see  Fig.  262)  and  the  meter  is 
underlagged.  This  means  that  the  resistance  R2  in  Fig.  272 
must  be  decreased.  After  the  change  in  Rz  has  been  made  the 
test  is  repeated,  and  so  on  until  the  two  constants  agree. 

If  the  current  had  been  leading,  0  negative,  the  result  would 
have  been 

COS  (—  0  +  a)  <  COS  (—  0) 

-  e  +  a  >  -  e. 

Here  a  must  be  a  negative  angle  and  the  meter  is  overlagged. 

In  this  connection,  attention  may  be  called  to  the  fact  that  the 
statement  that  a  power  factor  is  Q.5,  for  example,  may  give  little 
indication  of  the  conditions  under  which  the  meter  is  operating, 
for  both  the  P.D.  and  current  waves  may  be  irregular.  With  a 
distorted  P.D.  wave,  one  may  obtain  various  current  waves, 
depending  upon  the  method  of  regulation  which  is  used,  the  power 
factor  always  being  0.5.  For  instance,  if  inductances  be  used, 
the  upper  harmonics  in  the  current  wave  will  be  suppressed  to  a 
certain  extent.  If  the  change  from  unity  to  a  low  power  factor 
(0.5)  is  made  by  using  a  three-phase  circuit,  as  shown  on  page 
503,  the  fundamental  will  be  lagged  60°,  but  the  harmonics  will 
not  appear  in  their  proper  phase  relations. 

The  most  exacting  test  for  the  lagging  is  when  0  =  90°,  for 
in  that  case,  the  meter  will  register  unless  a  =  0.  It  is  difficult 
to  adjust  0  to  exactly  90°.  A  natural  method  is  to  take  the 
voltage  and  current  from  the  two  phases  of  a  two-phase  circuit, 
but  the  two  e.m.f  s  may  not  be  exactly  90°  apart  and  the  regulat- 
ing devices  together  with  the  current  coils  of  the  instruments 
may  shift  the  phase  of  the  current  slightly. 

Correct  lagging  is  especially  important  when  induction  meters 


478  ELECTRICAL  MEASUREMENTS 

are  used  for  measuring  energy  supplied  for  industrial  purposes. 
Induction  motors  which  are  commonly  used  may  be  only  par- 
tially loaded  and  therefore  operating  at  low  power  factors. 
This  is  the  condition  at  which  it  is  most  necessary  to  keep  the 
potential  and  current  fluxes  of  the  meter  in  the  proper  phase 
relation. 

Light -load  Adjustment. — The  principle  underlying  the  devices 
used  for  the  light-load  adjustment  is  that  of  the  shaded  pole 
motor.  In  this  type  of  motor  the  flux  from  the  stator  is  split 
into  two  portions  which  are  displaced  in  time  phase.  Con- 
sequently, the  forces  acting  upon  the  movable  element  are  un- 
balanced and  a  tendency  towards  rotation  results.  Referring 
to  Fig.  272,  which  shows  the  electric  and  magnetic  circuits  of 
one  type  of  watt-hour  meter  made  by  the  General  Electric  Co., 
PL  is  the  potential  lug.  Immediately  below  it  is  a  stamping  LLA 
which  forms  a  short- circuited  coil  of  a  single  turn;  it  is  made  of 
sheet  metal  of  the  appropriate  resistivity,  and  so  mounted  that 
it  can  be  displaced  in  its  own  plane  either  to  the  right  or  to  the 
left  by  moving  the  lever  L. 

Suppose  that  the  potential  coil  is  energized,  that  there  is  no 
load  on  the  meter  and  that  LLA  is  placed  symmetrically  with 
respect  to  the  potential  pole.  Currents  will  be  induced  in  LLA 
which  will  cause  a  back  magnetomotive  force,  but  as  LLA  is 
symmetrically  placed  with  respect  to  the  pole  tip,  the  flux  cut- 
ting the  disc  will  be  symmetrical  with  respect  to  the  pole  and  all 
in  the  same  time  phase.  Consequently  there  will  be  no  tendency 
for  the  disc  to  turn.  Now  suppose  the  loop  to  be  displaced  to- 
ward the  left — the  part  of  the  pole  covered  by  it  will  be  "  shaded," 
that  is,  owing  to  the  induced  currents  in  the  loop,  the  flux  from 
that  portion  of  the  pole  will  be  decreased  and  displaced  in  phase 
when  compared  with  that  from  the  unshaded  portion  at  the 
right  of  the  loop.  Thus  the  disc  is  acted  on  by  two  sets  of 
fluxes  which  differ  in  time  phase  and  there  is  a  travelling  field 
and  a  tendency  to  rotation.  By  giving  the  loop  the  proper 
displacement  the  friction  may  be  compensated  so  that  the  disc 
will  begin  to  move  as  soon  as  a  very  small  load  is  put  on  the 
circuit. 

Sources  of  Error  in  Induction  Watt-hour  Meters. — The  read- 
ings of  the  induction  watt-hour  meter  are  subject  to  a  number  of 


ELECTRICITY  METERS 


479 


errors  inherent  in  the  construction  of  the  instrument,  which  are 
not  found  in  instruments  based  on  the  electrodynamometer  prin- 
ciple. In  the  main,  these  errors  are  due  to  incorrect  phase  rela- 
tions of  the  various  fluxes  and  to  saturation  effects  in  the  iron. 
They  are  most  troublesome  at  low  power  factors  and  with  badly 
distorted  wave  forms.  The  following  curves  apply  to  a  single 
meter,  in  which  the  errors  were  much  exaggerated.  Unless 
otherwise  specified  the  wave  forms  contained  no  irregularities  or 
peaks. 

Temperature  Errors. — The  temperature  of  the  instrument  may 
be  altered  either  through  self-heating  or  change  of  room  tempera- 


1.04 


1.02 


1.00 


M. 


Induction  Watt-hour  Meter 
Effect  of  Temperature 
Frequency  =60  Cycles 
E  =110  Volts 
Smooth  Waves 


1C    20   30    40 


50    60    70    80 
Per  Cent  K.V.A.Load 


100   110   120   130 


FIG.  273. — Showing  effect  of  temperature  on  induction  watt-hour  meter. 

ture.  If  the  temperature  rises,  the  resistance  of  the  disc  increases 
so  that  while  the  driving  torque  is  decreased,  the  retarding  torque 
is  lessened  in  about  the  same  proportion,  the  two  effects  thus 
tending  toward  compensation.  There  are  certain  other  effects; 
for  instance,  the  drag  magnets  decrease  in  strength  and  as  their 
effect  depends  on  the  square  of  their  strength,  a  1  per  cent  change 
will  change  the  retarding  torque  2  per  cent.  The  resistances  of 
the  potential  and  lag  coils  change  and  disturb  the  lag  adjust- 
ment; the  permeability  of  the  iron  and  the  iron  losses  are  also 
changed.  The  net  effect  is  very  different  in  different  meters. 

The  effect  may  be  of  importance  in  the  use  of  portable  rotat- 
ing standard  watt-hour  meters.     With  some  types  of  such  meters 


480 


ELECTRICAL  MEASUREMENTS 


it  may  be  necessary  to  insert  a  thermometer  in  the  instrument 
in  such  a  manner  as  to  give  the  mean  temperature,  and  to  pro- 
vide a  calibration  card  which  will  give  the  necessary  corrections 
for  the  ordinary  range  of  atmospheric  temperature. 

Fig.  273  shows  the  effect  of  change  of  temperature  on  an  induc- 
tion watt-hour  meter  of  accepted  design. 

Frequency  Errors. — The  effect  of  a  departure  from  the  normal 
frequency  may  be  shown  qualitatively  as  follows. 

Suppose  that  the  frequency  is  doubled,  the  voltage,  current, 
and  power  factor  of  the  load  remaining  fixed.  Assuming  that 
the  resistance  of  the  potential  coil  is  small,  the  potential-coil  flux 
will  be  halved.  However,  the  currents  induced  in  the  disc  by  this 


1.08 

1.06 

1.04 

1.02 

1.00 

W  .98 

M.96 

1.94 


o-o, 


P.F.= 


Induction  Watt-hour  Meter 
Effect  of  Frequency  and  Overload 
Smooth  Waves 
50  Cycles 
60  Cycles 


70  Cycles 

110  Volts 


E 


0      10     20     30     40     50     60     70     80     90     100   110    120   130    140   150    ICO    170,  180    190  200 
Per  Cent  K..Y.  A. Load 

FIG.  274. — Showing  effect  of  frequency  on  induction  watt-hour  meter. 

flux  will  remain  as  before,  for,  while  the  flux  is  only  one  half 
as  great,  it  is  varying  at  twice  the  frequency.  The  induced  cur- 
rents react  with  the  current-coil  flux,  which  is  fixed.  The  net 
result  is  that  the  alteration  in  this  portion  of  the  accelerating 
torque  is  that  due  to  the  changed  time- phase  relation  of  the  fluxes. 
The  currents  induced  in  the  disc  by  the  current-coil  flux  are 
doubled,  for  though  the  value  of  the  flux  is  not  changed  it  is 
varying  at  twice  the  normal  frequency.  These  doubled  currents 
react  with  the  halved  potential-coil  flux,  so  again  the  effect  is 
that  due  to  the  changed  time- phase  relation  of  the  fluxes. 


ELECTRICITY  METERS 


481 


An  increase  in  frequency  will  also  change  the  distribution  and 
the  lag  of  the  currents  in  the  movable  member  and  increase  the 
impedance  of  the  disc. 

In  the  practical  case  a  change  of  frequency  upsets  the  lagging, 
that  is,  the  time-phase  relation  of  the  current  and  potential  coil 
fluxes,  which  has  been  adjusted  at  some  standard  frequency. 
This  being  so,  one  would  expect  that  the  effects  of  a  change  of 
frequency  would  not  be  very  marked  with  loads  of  unity  power 
factor  but  might  be  considerable  if  the  power  factor  were 
low.  Such  is  found  to  be  the  case;  see  Fig.  274  which  also 
shows  the  effect  of  an  overload  on  the  registration  at  normal 
frequency. 


1.04 
1.02 
1.00 

.98 
.96 

H.M 

fi.« 

J.90 

.88 
.80 
.84 
.82 
.80 

! 

t 

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ii 

^ 

i 

\ 

I 

/ 

\ 

\ 

^ 

x 

/ 

II 

\ 

^ 

/ 

^ 

3 

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A 

9 

A 

r\  / 

- 

\ 

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Yl 

A[ 

i 

\ 

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If 

A 

\ 

< 

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D 

i 

Induction  Watt-hour  Met* 
Effect  of    Wave  Form 
Frequency=60  Cycles 
E  =110  Volts 
1  =  9.3  Amps. 
Current  and  Voltage  Waves  ] 
Current  Wave  Only  Irregulai 

?r 

rre£ 

1 

1/V 

\j 

i- 
ii- 

1 

10    20   a 

3     40     50    .60     70     80     90    100    90     80     70     60     50     40    30     20 
Lag                             Power  Factor                                     Lead 

jjug  .rower  racior  AJCUU 

FIG.  275 A. — Showing  effect  of  poor  wave  form  on  the  registration  of  an 

induction  meter. 

Effect  of  Wave  Form. — As  the  registration  is  affected  by  varia- 
tions in  frequency,  one  naturally  expects  that  changes  of  wave 
form  will  affect  the  accuracy  of  the  meter,  especially  at  low  power 
factors.  This  is  shown  by  the  curve, 'Fig.  275^4. 

The  theory  of  the  induction  wattmeter  given  on  page  452  rests 
on  the  assumption  of  sinusoidal  waves  of  current,  voltage  and 
flux.  As  the  flux  wave  is  the  time  integral  of  the  voltage  wave, 
the  form  of  the  flux  wave  due  to  the  potential  coil  will  not  be  the 

31 


482  ELECTRICAL  MEASUREMENTS 

same  as  that  of  the  voltage  applied  at  the  potential  terminals  un- 
less the  last  be  sinusoidal.  The  currents  induced  in  the  disc  by 
the  current  coils  depend  on  the  time  rate  of  change  of  the  flux 
due  to  the  current  coils  and  will  differ  from  the  current  wave  in 
form  unless  this  form  be  sinusoidal. 

When  the  circuit  conditions  are  such  that  the  wave  form  is 
greatly  distorted,  this  source  of  error  may  give  rise  to  inaccura- 
cies in  metering,  the  reasons  for  which  become  apparent  only 
when  the  wave  form  has  been  determined  by  an  oscillograph  or 
other  wave-tracing  device. 

In  a  certain  case  of  this  kind  where  induction  meters  persist- 
ently refused  to  operate  correctly,  in  spite  of  the  fact  that  fac- 
tory tests  showed  them  to  be  commercially  correct,  it  was  found 
that  the  e.m.f.  wave  form  was  as  shown  in  Fig.  2755. 


FIG.  275B. — PD.  wave.  When  the  generator  was  connected  to  a  trans- 
mission line  the  wave  form  was  so  badly  distorted  that  induction  meters 
could  not  be  relied  upon. 

Effect  of  Voltage  Variation. — Departure  of  the  voltage  from  its 
normal  value  may  influence  the  accuracy  of  the  meter  because  of 
change  in  the  resistance  of  the  potential  coil  winding  and  of 
saturation  effects  in  the  iron  core  of  the  potential  coil.  For  the 
ordinary  range  of  voltages  on  a  circuit  which  is  nominally  operated 
at  a  constant  potential,  these  effects  will  not  be  large.  This  is 
illustrated  by  Fig.  276. 

Polyphase  Watt-hour  Meters. — For  metering  in  polyphase 
circuits  where  the  two-wattmeter  method  is  applicable,  a  special 
form  of  induction  watt-hour  meter  has  been  developed.  An 
example  of  this  is  shown  in  Fig.  277. 

The  instrument  consists  of  two  complete  induction  watt-hour 
meters  mounted  in  the  same  case  and  with  the  two  discs  rigidly 


ELECTRICITY  METERS 


483 


fastened  to  the  same  shaft.  The  driving  torque  is  therefore  the 
sum  of  the  torques  due  to  the  two  members;  that  is,  it  is  propor- 
tional at  any  instant  tg  the  power  in  the  circuit.  The  retarding 


1.06 
1.04 
1.02 

:i.oo 


.94 


Induction  Watt-hour  Meter 

Effect  of  Voltage  Variation 

Frequency  =  60  Cycles 

Smooth  Waves 


70    80 


90   100   110   120   130   140   150 
Volts 


FIG.  276. — Showing  effect  of  voltage  variation  on  induction  watt-hour  meter. 


FIG.  277. — Polyphase  watt-hour  meter,  Westinghouse  Co. 

torque  is  furnished  by  two  sets  of  drag  magnets,  one  applied  to 
each  disc.  Of  course,  there  must  be  no  interference  between 
the  two  elements. 


484  ELECTRICAL  MEASUREMENTS 

Each  element  is  complete  in  itself  and  must  be  adjusted  so 
that  it  registers  correctly  at  both  high  and  low  loads,  as  well 
as  at  both  unity  and  low  power  factors.  It  is  essential,  when 
carrying  out  these  adjustments,  that  both  potential  circuits  be 
kept  energized,  otherwise  the  moving  element  will  experience  an 
abnormal  retarding  torque. 

Suppose  the  upper  element  to  be  under  adjustment;  both  sets  of 
drag  magnets  are  placed  in  what  seems  to  be  a  reasonable  posi- 
tion and  the  adjustment  is  made  as  in  a  single-phase  meter. 
When  it  is  completed,  attention  is  given  to  the  lower  element,  the 
constant  of  which  must  be  varied  and  made  equal  to  that  of  the 
upper  element  without  changing  the  constant  of  the  latter. 

It  is  not  permissible  to  change  the  position  of  the  drag  magnets  ; 
the  change  in  the  constant  must  be  effected  by  altering  the  driv- 
ing torque  of  the  lower  element.  This  may  be  done  by  varying 
the  fluxes  and  for  this  purpose  taps  are  sometimes  brought  out 
from  the  potential  coil  by  which  the  number  of  active  turns  may 
be  altered.  In  the  induction  meters  now  made  by  the  General 
Electric  Co.,  this  adjustment  is  effected  by  changing  the  posi- 
tion of  the  lower  current  coils  by  means  of  a  screw. 

A  very  good  check  on  the  equality  of  the  two  elements  may  be 
obtained  by  operating  the  potential  circuits  in  parallel  and  the 
current  circuits  in  series  and  opposed;  under  these  conditions  the 
disc  should  not  rotate. 

When  induction  meters  are  used  on  loads  which  have  a  recti- 
fying effect,  such  as  three-phase  arc  furnaces,  they  must  be  in- 
serted in  the  primary  of  the  transformer  which  supplies  the  load. 

MERCURY  MOTOR  METERS 

The  principle  utilized  in  the  mercury  motor  meters  is  that 
illustrated  by  the  familiar  Barlow's  wheel,  in  which  a  current 
flows  radially  in  a  pivoted  copper  disc  so  placed  between  the 
poles  of  a  magnet  that  it  is  cut  by  the  flux.  On  the  passage  of  the 
current  the  disc  is  set  in  rotation. 

The-advantages  of  the  mercury  motor  meter  for  direct  current 
are  the  elimination  of  the  commutator,  as  well  as  the  wire-wound 
armature  and  the  brushes,  and  the  decrease  of  the  wear  on  the 
lower  pivot  and  jewel.  These  things  tend  to  decrease  the  expense 
of  maintenance. 


ELECTRICITY  METERS 


485 


A  practical  difficulty  has  been  that,  in  time,  the  mercury 
is  very  likely  to  become  contaminated  and  cause  an  increase  in 
the  friction  of  the  meter. 

The  Mercury  Ampere-hour  Meter. — Aside  from  special  uses, 
some  of  which  will  be  referred  to  later,  ampere-hour  meters  are 
intended  for  use  on  constant-potential  circuits,  for  if  the  potential 
be  kept  constant  their  readings  form  as  just  a  basis  for  that  part  of 
the  charges  which  are  dependent  on  the  amount  of  energy 
furnished  as  do  those  of  the  watt-hour  meter.  When  the  ampere- 
hour  meter  is  so  used,  the  register  is  graduated  to  read  in  kilowatt- 
hours,  the  voltage  of  the  circuit  having  some  definite  value. 

In  America  the  watt-hour  meter  is  now  used  almost  exclusively 
in  lighting  installations,  but  in  Great  Britain  the  ampere-hour 
meter  is  extensively  employed. 


FIG.  278. — Working  parts  of  Ferranti  ampere-hour  meter. 

Ferranti  Ampere-hour  Meter. — The  Ferranti  ampere-hour 
meter  was  one  of  the  earliest  forms  of  electricity  meters,  its 
development  having  been  begun  as  early  as  1883. 

Fig.  278  shows  the  essential  parts  of  this  meter  as  at  present 
constructed.  The  motor  is  of  the  Faraday  disc  type. 


486  ELECTRICAL  MEASUREMENTS 

The  current  enters  at  the  +  terminal  Ci,  flows  through  the 
mercury  to  the  amalgamated  edge  of  the  copper  disc  CD,  then 
through  the  disc  to  its  central  portion,  which  is  amalgamated,  and 
out  by  the  terminal  C2.  Thus  the  current  in  the  disc  is  in  the 
field  of  the  permanent  magnets  SD  and  a  driving  torque  is  imparted 
to  the  disc  armature.  To  protect  the  copper  from  the  action  of 
the  mercury  the  top  and  bottom  surfaces  of  the  disc  are  platinum- 
plated  and  enameled,  except  directly  above  C2.  As  the  arma- 
ture moves  through  the  fields  of  the  two  magnets  SB  and  SD, 
there  will  be  the  usual  braking  action  due  to  eddy  currents.  The 
fluid  friction  of  the  mercury  also  contributes  a  retarding  action  and 
as  this  increases  with  the  speed,  that  is,  with  the  customer's  load, 
the  meter  is  compounded  by  a  coil  of  a  few  turns,  CC,  on  the 
lower  iron  crossbar.  When  the  current  is  increased,  the 
strength  of  the  field  SD  is  also  increased  and  hence  the  driving 
torque  becomes  larger.  However,  the  action  of  the  magnetic 
brake  remains  the  same,  for  the  poles  at  SD  are  so  arranged 
that  when  the  field  at  SD  is  increased  that  at  SB  is  diminished. 

The  buoyancy  of  the  armature  is  adjusted  by  a  weight  on  the 
spindle  until  the  disc  just  sinks.  Friction  between  the  pivot  and 
jewel  is  thus  reduced  to  a  minimum.  A  sealing  device  is  used  so 
that  the  mercury  will  not  be  spilled'  during  transportation. 

Sangamo  Meter. — In  America  the  mercury  motor  meter  has 
been  developed  by  the  Sangamo  Electric  Co.  which  began  the 
work  in  1904. 

The  main  body  of  the  mercury  chamber  is  made  of  a  moulded 
insulating  compound  (see  Fig.  279).  The  two  current  terminals, 
Eit  EZ,  are  diametrically  opposite  each  other,  and  above  the  lower 
part  of  the  chamber  which  contains  the  copper  disc  armature 
is  a  spirally  laminated  ring  of  soft  iron  (return  plate).  On 
the  spindle  above  the  disc  is  a  hardwood  float;  this  takes  the 
pressure  from  the  lower  bearing,  which  becomes  merely  a  guide; 
in  fact,  a  slight  thrust  is  exerted  against  the  bearing  plate  of  the 
upper  ring  jewel. 

In  all  Sangamo  meters  the  copper  armature  discs  are  now  slit 
radially.  The  current  is  thus  caused  to  flow  directly  from  ter- 
minal EI  to  Ez  without  spreading  over  the  disc.  By  this  means 
the  torque  is  increased  about  40  per  cent. 

The  cover  of  the  mercury  chamber  is  made  with  a  central  tube 


ELECTRICITY  METERS 


487 


projecting  downward.  The  clearance  of  the  spindle  in  the  tube 
is  about  0.006  in.  and  the  form  of  the  chamber  is  such  that  the 
mercury  cannot  be  spilled  even  though  the  instrument  be 
inverted. 

As  the  current  flows  diametrically  across  the  disc,  the  flux  must 
be  directed  upward  on  one  side  of  the  spindle  and  downward  on 
the  other  side.  The  driving  field  is  furnished  by  either  a  perma- 
nent or  an  electro-magnet,  according  to  circumstances;  the 


Upper  Bearing 
Screw 


Arch. 


pward  Thrust  of 
Moving  Element  only  i  Oun^ 
This  is  the  only  Actual  Bearing 

Insulation  ^Damping  Disc 


Clamp  King 

Magnet  Holding  Ear          Pole  'Plate 

FIG.  279. — Section  of  working  parts  of  Sangamo  meter. 

poles  are  immediately  beneath  the  chamber  and  contiguous  to 
the  current  lugs.  The  magnetic  circuit  is  completed  by  the 
spirally  laminated  soft  iron  return  plate.  The  necessary  "  brak- 
ing" action  is  due  to  induced  currents  in  the  armature  disc  and 
in  the  usual  aluminum  damping  disc  provided  for  that  purpose. 
The  Sangamo  Ampere-hour  Meter. — Aside  from  the  ordinary 
lighting  and  power  installations,  there  are  certain  operations, 
such  as  electroplating  and  the  charging  and  discharging  of 
storage  batteries,  where  it  is  desirable  to  register  the  total  quan- 
tity of  electricity  rather  than  the  energy.  For  this  purpose,  the 


488 


ELECTRICAL  MEASUREMENTS 


Sangamo  ampere-hour  meter  has  been  developed.     In  this  instru- 
ment the  driving  field  is  produced  by  a  large  permanent  magnet. 
In    electric    automobile    and    truck    work,    an    ampere-hour 
meter  will  give  an  indication  of  the  state  of  charge  of  the  battery. 


FIG.  280. — Sangamo  ampere-hour  meter. 

The  Mercury  Watt -hour  Meter. — The  electrical  connections  for 
the  Sangamo  direct- current  watt-hour  meter  are  shown  in  Fig. 
281  A.  The  main-line  current  passes  across  the  copper  armature 
disc  in  the  direction  EiE^.  The  U-shaped  electromagnet  Y, 
which  furnishes  the  necessary  field,  is  connected  across  the  line. 

The  light-load  adjustment  is  obtained  by  the  use  of  a  thermo- 
couple H  which  is  inserted  in  a  shunt  circuit  between  E±  and  E^ 
and  heated  by  a  resistance  coil  which  forms  a  part  of  the  potential 
circuit  of  the  meter.  The  couple  sends  a  small  current  through 
the  disc  in  the  same  direction  as  the  load  current.  The  effect  of 
the  thermo-couple  is  controlled  by  altering  the  position  of  the 
connecting  link  K.  The  couples  are  now  made  reversible,  so 
that  the  same  meter  may  be  used  in  either  the  positive  or  nega- 
tive side  of  the  line. 

As  the  fluid  friction  naturally  becomes  unduly  large  with  in- 
crease of  armature  speed,  the  instrument  is  compounded  by  taking 
the  main  circuit  around  the  U-magnet  at  CT.  This  improves 
the  action  of  the  instrument  at  heavy  load  and  at  overload. 


ELECTRICITY  METERS 


489 


For  high  capacities,  meters  of  10  amp.  are  used  with  shunts 
provided  with  heavy  connecting  cables.  For  obtaining  the  -final 
adjustment  of  the  multiplying  power  of  the  shunt  the  high- 
resistance  wire  N  and  sliding  terminal  T  are  provided. 

The  full-load  drop  through  the  armature  of  a  10-ampere  meter 
without  a  shunt  is  about  30  millivolts;  in  the  20  to  80-ampere 
meters  with  internal  shunts  it  is  about  60  millivolts;  for  the 


A  B 

FIG.  281. — Sangamo  direct-current  watt-hour  meter. 

external  shunts  the  drop  is  about  75  millivolts.  This  higher 
drop  is  necessitated  by  the  resistance  of  the  connecting  cables. 
The  loss  in  the  potential  circuit  of  a  110-volt  meter  is  about  4.5 
watts;  with  220- volt  and  550- volt  meters  it  is  about  9  and  22 
watts,  respectively.  In  the  two  latter,  the  larger  part  of  the  loss 
is  in  the  added  wire  resistance.  The  full-load  torque  is  about  6 
cm.-gm. 

In  this  meter  the  drag  magnets  are  fixed  in  position,  and  a  25 
per  cent  variation  in  the  braking  action  may  be  obtained  by 
the  use  of  a  magnetic  shunt  on  the  drag  magnets.  The  shunt 


490  ELECTRICAL  MEASUREMENTS 

is  a  disc  of  soft  iron  mounted  on  a  fine- pitched  screw,  as  shown 
at  X,  Fig.  2815.  The  drag  magnets  are  shielded  by  the  cast-iron 
frame  of  the  instrument. 

The  ability  of  the  Sangamo  meter  to  withstand  severe  mechan- 
ical shocks  and  jars  and  its  freedom  from  the  influence  of  stray 
fields,  which  if  they  do  cut  the  armature  are  directed  either  up- 
ward or  downward  on  both  sides  of  the  spindle,  render  it  appli- 
cable to  car  tests  in  street-railway  work.  For  this  purpose  a 
special  form  of  register,  with  a  resetting  device  for  registering 
the  consumption  of  energy  during  a  single  trip,  has  been  devel- 
oped. The  register  has  also  the  ordinary  totalizing  dials. 
• 

METER  TESTING 

To  maintain  the  accuracy  of  the  meters  in  any  distribution 
system,  it  is  necessary  that  they  be  tested  periodically.  On  ac- 
count of  the  risk  of  altering  the  constant  of  any  form  of  motor- 
meter  during  transportation  all  tests  must  of  course  be  made  on 
the  meters  as  installed. 

In  many  States,  laws  have  been  enacted  which  permit  a  cus- 
tomer, in  case  he  is  dissatisfied  with  his  bill,  to  request  the  ser- 
vices of  the  appropriate  public  service  commission  in  order  that 
a  test  may  be  made  by  a  disinterested  party. 

Referring  to  the  fundamental  formula  for  the  watt-hour  meter, 
(page  461),  for  meters  as  actually  constructed,  the  watt-hours 
registered  =  Kh  times  (number  of  revolutions  of  disc).  Kh  is 
the  watt-hour  constant  of  the  meter;  its  value  is  usually  marked 
on  the  meter  disc.  In  some  types  of  meters  the  constant  is  ex- 
pressed in  watt-seconds  on  the  dials  for  each  revolution  of  the  disc. 
In  any  case  the  constant  K  is  a  fixed  ratio  depending  on  the  ar- 
rangement and  ratio  of  worm,  wormwheel,  gear  train,  and  the 
dial  units  of  the  watt-hour  meter.  In  any  meter  tests  which  are 
made  by  timing  the  disc  as  it  rotates  one  must  be  certain  that 
the  register  used  on  the  meter  has  the  proper  constant. 

In  case  of  a  dispute  between  the  customer  and  a  supply  com- 
pany the  meter  must  be  tested  as  found,  that  is  before  any  ad- 
justments are  attempted.  The  records  of  these  tests  are  neces- 
sary in  order  that  the  customer  and  the  company  may  arrive  at 
an  understanding. 

To  test  a  watt-hour  meter,  it  is  necessary  merely  to  determine 

. 


ELECTRICITY  METERS  491 

the  rate  of  revolution  of  the  disc,  then  multiply  this  value  by  the 
test  constant  of  the  meter,  and  compare  the  result  with  the 
number  of  watts  indicated  by  standard  instruments  which  are  so 
connected  in  the  circuit  as  to  measure  the  same  amount  of 
power  as  the  watt-hour  meter  under  test.  The  energy  is  sup- 
posed to  be  supplied  at  a  constant  rate; 

n,       KhN3,QW 

watts  by  watt-hour  meter  =  P    =  -    —  -  — 

c 

For  direct-current  meters: 

Correct  watts  =  P  =  VI; 

N  =  number  of  revolutions  of  the  disc. 
t  =  time  in  seconds  for  N  revolutions. 

V  =  corrected  average  voltage  measured  at  the  potential  ter- 
minals of  the  meter. 

/  =  corrected  average  current  flowing  through  the  series  coils 
of  the  watt-hour  meter. 

If  the  voltage  and  current  fluctuate  badly,  VI  should  be  the 
average  watts  during  the  test. 

If  a  three-wire  meter,  with  the  potential  circuit  connected  be- 
tween one  side  of  the  main  circuit  and  the  neutral  wire,  is  cali- 
brated with  both  current  coils  connected  in  series,  then  the  value 
of  Khto  be  used  in  the  above  formulaforP'  is  one  half  that  marked 
on  the  disc. 

The  different  manufacturers  of  meters  use  various  modifica- 

tions of  the  fundamental  formula,  and  one  should  be  sure  that 

the  test  constant  given  by  the  maker  is  used  in  the  proper  manner. 

To  illustrate,  for  all  meters  made  by  the  General  Electric  Co., 

watt-hour  constant  =  test  constant. 

g,JV3,600. 

Kh  =  Kt  r    —  -     —  -  — 

For  Fort  Wayne  meters,  type  K,  watt-hour  constant  = 
test  constant 


For  the  Fort  Wayne  meters,  types  K\y  K2,  Ks,  K^  watt-hour 
constant  =  test  constant 


, 

f  ^~A 


492                 ELECTRICAL  MEASUREMENTS 
For  Sangamo  meters,  watt-hour  constant  = Q~AnrT 

Kh  =  3,600  P'         t 

For  Duncan  meters,  watt-hour  constant  =  test  constant 

Kh  =  Kt  P'  = 

i 

-pi      T1rr    ,.     ,  test  constant 

1H  or  Westmghouse  meters,  watt-  hour  constant  = 

o,bUU 

Kh  =  3,600  Pf      ~T 

except  for  type  CW—  6,  for  which  watt-hour  constant  =  test 
constant 

Kh  =  Kt  P'  = 


t 

The  watt-second  constant,  Ks,  is  the  number  of  watt-seconds 
of  energy  necessary  to  cause  one  revolution  of  the  movable  ele- 
ment. It  is  equal  to  the  watt-hour  constant  multipled  by  3,600, 
the  number  of  seconds  in  an  hour.  • 

The  register  constant,  Kr,  is  the  factor  by  which  the  reading 
of  the  register  must  be  multiplied  in  order  to  ascertain  the  total 
amount  of  electrical  energy  which  has  been  supplied  to  the  load 
via  the  meter.  For  meters  of  small  size,  such  as  are  used  in  the 
majority  of  cases,  the  modern  practice  is  to  make  this  factor  unity, 
for  it  is  likely  that  the  small  consumer  will  fail  to  understand  why 
the  supply  company,  in  making  out  his  bill,  should  multiply  his 
meter  reading  by  a  factor  of  2  or  4  for  instance.  In  meters  of 
large  size,  it  is  necessary  to  use  register  constants  of  10,  100  and 
so  on,  for  otherwise  the  value  in  kilowatt-hours  of  one  dial  divi- 
sion becomes  too  large. 

The  register  ratio,  Rr,  is  the  number  of  revolutions  of  the 
wheel  meshing  with  the  worm  or  pinion  on  the  shaft  of  the  movable 
element,  which  is  necessary  to  cause  the  first  or  most  rapidly 
moving  dial  hand  to  make  one  revolution. 

The  gear  ratio,  Rg,  is  the  number  of  revolutions  of  the  movable 
element  required  to  cause  the  first  dial  hand  to  make  one 
revolution. 


ELECTRICITY  METERS  493 

Common  Sources  of  Inaccuracy. — If  the  meter  is  very  slow, 
or  cannot  be  brought  up  to  speed,  the  trouble  may  be  due  to: 

1.  Commutator  and  brushes  pitted,  oily  and  dirty. 

2.  Commutator  segments  short  circuited. 

3.  Lint  or  magnetic  particles  between  drag  magnet  and  disc. 

4.  Disc  may  not  run  true,  or  may  be  out  of  position. 

5.  Pivot  worn. 

6.  Jewel  rough  or  cracked. 

7.  Dirt  in  jewel. 

8.  Undue  friction  in  the  worm  and  the  registering  train. 

9.  Upper  guide  bearing  pressed  down  on  shoulder  of  spindle. 

The  meter  may  register  too  much,  due  to  weakening  of  the 
magnets,  through  ageing  or  by  a  short  circuit  on  the  customer's 
premises. 

Methods  of  Testing. — There  are  several  methods  of  making 
tests  to  determine  whether  the  meter  is  registering  correctly  or 
not.  They  differ  in  the  arrangement  employed  for  ascertaining 
the  true  amount  of  power  or  energy  delivered  to  the  load  via  the 
meter.  The  arrangements  commonly  used  for  this  purpose  are: 

1.  Indicating  instruments. 

2.  A  calibrated  load  box  together  with  a  voltmeter. 

3.  A  rotary  standard  watt  hour  meter. 

When  indicating  instruments  or  a  calibrated  resistance  are 
employed,  the  time  in  seconds  required  for  a  whole  number  of 
revolutions  of  the  moving  element  of  the  watt-hour  meter  is 
determined  by  means  of  a  stop  watch.  In  direct-current  work, 
calibrated  ammeters  and  voltmeters  of  the  moving-coil  type  are 
used  to  determine  the  true  watts.  In  alternating- current  work 
a  calibrated  indicating  wattmeter  is  used.  If  small  meters  are 
tested,  one  must  be  sure  that  the  results  are  not  complicated  by 
the  loss  occurring  in  th6  voltmeter  or  in  the  potential  coil  of  the 
indicating  wattmeter.  The  watts  given  by  the  meter  are  calcu- 
lated by  the  appropriate  test  formula  and  compared  with  the 
results  given  by  the  indicating  instruments.  "The  percentage 

of  accuracy"  is  given  by  "  s  X  100.     The  "rate"  of  the 

true  watts 

meter  watts 

meter  is  given  by  -  — 

J    true  watts 


494 


ELECTRICAL  MEASUREMENTS 


In  carrying  out  the  test  the  meter  should  be  timed  for  as  much 
as  60  sec.  if  accurate  results  are  desired.  This  tends  to  reduce 
the  errors  due  to  the  personal  equation  in  timing  and  counting 
as  well  as  the  errors  due  to  the  stop  watch. 

Great  care  must  be  exercised  in  the  purchase  and  in  the  main- 
tenance of  the  stop  watches,  for  they  are  the  weakest  element  in 
this  method  of  testing.  A  watch  may  keep  good  time  but  be  in- 
accurate as  a  stop  watch.  It  is  important  that  the  indicating 
hand  start  and  stop  promptly  without  jumping  and  reset  to  ex- 
actly zero.  The  starting  and  stopping  errors  are  of  great  im- 
portance. In  order  that  one  may  be  sure  that  the  watch  is  in 
good  condition,  it  should  be  tested  at  several  points  before  be- 
ginning work. 

The  index  hand  of  a  stop  watch  moves  forward  by  a  succes- 
sion of  jumps  separated  by  intervals  during  which  the  hand  is  at 
rest,  so  that  though  the  watch  beats  J^  sec.,  the  hand  is  in 

motion  only  about  J-foo  sec.  at  each 
beat,  that  is,  while  the  escapement  is 
in  action.  There  is  thus  a  possibility 
of  an  error  of  nearly  %  sec.  due  to 
the  peculiar  mechanism  of  the  watch. 
In  timing  for  30  sec.,  this  might  give 
rise  to  an  error  of  about  two-thirds 
of  1  per  cent.,  in  addition  to  all  the 
other  errors  due  to  the  imperfect 
mechanical  action  of  the  mechanism 
and  the  personal  equation  of  the 
observer. 

Load  Boxes. — A  calibrated  load  box 
is  frequently  used  in  testing  meters  of 
small  size.  Such  an  arrangement  is 
shown  in  Fig.  283. 

The   coils   should  be  wound   non- 


FIG.  283. — Load  box  for 
meter  testing. 


inductively,  so  that  the  box  is  applicable  to  both  direct  and 
alternating-current  circuits.  The  resistance  material  should  have 
a  very  low  temperature  coefficient.  The  switches  should  be  of 
such  a  construction  that  contact  resistances  are  reduced  to  a 
minimum.  The  box  is  tested  in  the  laboratory  with  different 
combinations  of  switches  and  under  a  series  of  applied  voltages 


ELECTRICITY  METERS  495 

differing  by  0.5  volt.  Therefore,  when  it  is  used  on  a  test,  it 
is  necessary  only  to  observe  the  applied  voltage  in  order  to  de- 
termine the  load  on  the  meter.  It  is  to  be  noted  that  a  1  per 
cent,  error  in  the  voltage  reading  will  cause  a  2  per  cent,  error 
in  the  watts. 

The  resistor  in  the  box,  shown  in  Fig.  283,  consists  of  four 
units,  two  having  a  resistance  of  approximately  220  ohms  each, 
and  two  having  a  resistance  of  about  22  ohms  each.  The  follow- 
ing loads  may  be  obtained : 

At  110  volts  At  220  volts 

25  watts  approximately  100  watts  approximately 

50      "  1,000     " 

100      " 

250      " 

500      " 

1,000      " 

The  connecting  cables  are  included  in  the  measurement  when 
the  box  is  calibrated.  They  should  be  composed  of  a  large  num- 
ber of  fine  wires  so  that  they  may  be  very  flexible  and  in  order 
that  the  effect  of  a  break  in  any  individual  wire  may  be  small. 

When  such  a  load  box  is  used  for  routine  tests,  it  is  accompanied 
by  a  calibration  card  which  gives  the  watts  corresponding  to 
various  applied  voltages.  The  advantage  of  this  method  of 
testing  in  direct-current  work  is  that  it  is  necessary  to  provide  and 
to  read  only  one  instrument. 

Portable  Standard  Watt-hour  Meters. — Routine  tests  are  fre- 
quently much  facilitated  by  using  a  standard  watt-hour  meter 
instead  of  an  indicating  wattmeter  and  a  stop  watch.  The 
standard  is  a  portable  watt-hour  meter  with  a  special  register, 
readable  to  0.01  of  a  revolution,  which  allows  the  number  of 
revolutions  of  the  movable  element  to  be  read  witji  precision. 
This  register  must  be  so  arranged  that  it  may  be  promptly  started 
and  stopped  by  the  use  of  a  push  button. 

In  case  such  an  instrument  is  used,  after  having  connected  its 
current  coils  in  series  and  its  potential  coils  in  parallel  with  those 
of  the  meter  under  test,  one  has  only  to  compare  the  number  of 
revolutions  made  by  the  standard  during  a  certain  time  with 
the  number  made  by  the  meter  under  test  during  an  equal  time, 
for  example,  that  required  for  a  definite  number  of  revolutions 


496  ELECTRICAL  MEASUREMENTS 

of  the  meter  under  test,  and  then  allow  for  the  meter  constants. 
For  example,  denote  by  x  the  meter  under  test,  and  by  s,  the 
standard  meter.  The  average  powers  given  by  the  two  meters 
are  Px  and  Ps  ;  then 


x  t  * 

The  "  percentage  of  accuracy"  is  §*  100  =  f 

*    8  (Kh)sl\  S 

It  would  be  an  obvious  convenience  if  the  meters  had  equal 
watt-hour  constants. 

The  advantages  of  this  method  are  the  elimination  of  the  use 
of  the  stop  watch  by  the  tester,  independence  of  load  and  vol- 
tage fluctuations,  and  the  reduction  of  the  working  force,  for 
only  one  man  is  necessary.  Independence  of  load  and  voltage 
variations  is  a  most  decided  advantage,  for  at  times,  especially 
if  high-capacity  meters  are  being  tested,  it  is  necessary  to  use 
the  consumer's  load,  and  this  may  be  fluctuating. 

Rotary  standards  are  now  made  for  both  alternating  and  direct 
currents. 

The  alternating-current  standard  is  started  and  stopped  by 
making  and  breaking  the  potential  circuit.  In  the  direct- 
current  instrument  the  potential  circuit  is  kept  closed  so  that  the 
armature  and  disc  rotate  continuously;  the  register  is  thrown  into 
and  out  of  gear  by  an  electrically  operated  clutch. 

It  is  essential  that  the  construction  of  rotary  standards  be 
such  that  their  accuracy  will  not  be  affected  by  the  necessary 
handling  during  transportation.  This  means  that  the  geometry 
of  the  coil  system  and  of  the  brake  must  not  alter,  and  that  the 
friction  must  remain  constant.  To  insure  this  last  it  is  neces- 
sary to  provide  means  for  raising  and  clamping  the  movable 
system  so  that  the  pivots  and  jewels  may  not  be  injured. 

To  reduce  the  irregularities  due  to  unavoidable  friction,  the 
commutators  used  in  direct-current  standards  should  be  of  small 
diameter  and  the  brush  pressure  constant.  A  high  ratio  of  torque 
to  weight  of  the  moving  element  is  most  desirable. 

When  the  instrument  is  connected  into  the  circuit,  care  should 
be  taken  that  the  field  and  the  armature  coils  are  at  practically 
the  same  potential,  especially  if  the  voltage  is  so  high  that  a 
multiplier  is  used. 


ELECTRICITY  METERS 


497 


For  the  greatest  utility,  the  current  range  of  the  rotary  stand- 
ard should  be  large,  so  that  it  may  be  used  for  testing  meters  of 
a  number  of  different  capacities.  At  the  same  time,  the  ampere- 
turns  due  to  the  fixed  coils  must  be  large  even  when  small  meters 
are  tested.  This  insures  that  the  standard  will  never  be  operated 
on  what  is  the  equivalent  of  a  light  load.  Therefore,  the  cur- 
rent coils  must  be  wound  in  sections  so  arranged  that  they  can 
conveniently  be  connected  in  various  series-parallel  combina- 
tions by  some  reliable  means.  The  full-load  ampere-turns  of  all 
the  sections  should  be  the  same. 


FIG.  284. — Rotating  standard  watt-hour  meter  for  direct  currents, 
General  Electric  Co. 

Large  electrical  companies  now  use  rotary  standards,  which  are 
accurately  maintained  by  their  laboratory  departments,  as  sec- 
ondary standards  when  checking  and  adjusting  service  meters  be- 
fore they  are  sent  out  for  installation  on  the  consumer's  premises. 

While  the  rotary  standard  is  very  convenient  and  in  some 

32 


498 


ELECTRICAL  MEASUREMENTS 


cases  necessary,  one  must  not  forget  that  great  care  must  be 
taken  if  accurate  results  are  to  be  obtained. 

The  direct-current  instrument  is  heavier  and  less  convenient 
than  that  for  alternating  current,  and  is  not  so  commonly  used. 
When  the  instrument  is  calibrated,  and  when  it  is  used,  it  is 


FIG.  285. — Rotating  standard  watt-hour  meter  for  alternating  currents, 
Westinghouse  Co. 

. 

necessary  to  keep  the  potential-coil  circuit  of  a  direct-current 
rotary  standard  energized  for  a  considerable  time  (about  30 
min.)  before  any  readings  are  taken— long  enough  for  the  entire 
armature  circuit,  the  disc,  and  the  drag  magnets  to  attain  their 
permanent  states  of  temperature,  since  the  resistance  of  the 
armature  circuit,  the  resistance  of  the  disc  to  eddy  currents  and 


ELECTRICITY  METERS 


499 


the  strength  of  the  drag  magnets  are  all  dependent  upon  tem- 
perature. The  heat  liberated  in  the  current  coils  also  influences 
the  accuracy  of  the  meter  for  it,  too,  affects  the  temperature  of 
the  potential  coil,  the  disc  and  the  drag  magnets.  This  self- 
heating  error  may  be  of  importance  in  careful  tests  if  the  meter  is 
so  used  that  it  must  carry  a  large  current  for  a  long  time.  The 
alternating-current  standard  is  subject  to  the  errors  found  in 
meters  of  the  induction  type  (see  pages  478,  505).  Therefore, 
in  case  of  a  serious  dispute  between  the  consumer  and  the  supply 
company,  it  is  preferable  to  use  indicating  instruments  if  possible. 


a 


Source 


FIG.  286. — Timing  device  for  calibrating  watt-hour  meters. 

The  use  of  rotary  standards  takes  the  determination  of  the 
time  element  from  the  tester,  who  must  of  necessity  use  a  stop 
watch,  and  hands  it  over  to  the  laboratory  department,  where 
much  more  accurate  timing  devices  may  be  maintained. 

A  timing  device  designed  for  use  in  calibrating  rotary  stand- 
ards is  shown  diagrammatically  in  Fig.  286. 

The  master  clock  which  operates  the  device  has  a  pendulum 
which  beats  seconds  (%  period).  At  each  beat  of  the  pendulum 
the  relay  contact  is  made  and  the  ratchet  wheel  is  advanced 
one  tooth,  carrying  with  it  the  contact  sector  e.  The  duration 
of  the  contact  of  the  spring  b  corresponds  to  36  teeth  on  the  rat- 
chet wheel,  in  other  words,  to  36  sec.  The  potential  circuit, 


500 


ELECTRICAL  MEASUREMENTS 


a  to  d,  operates  the  clutch,  if  direct-  current  meters  are  being 
tested.  With  alternating-current  meters,  as  shown  in  the  figure, 
the  contact  sector  e  is  included  in  the  potential  circuit.  In  either 
case,  the  power  by  the  meter  is 

P  = 


Fictitious  Loads  and  Arrangements  for  Phase  Shifting.  —  In 
the  laboratory  it  is  often  convenient,  and  sometimes  necessary, 
especially  when  meters  of  high  capacity  are  tested,  to  avoid  the 
consumption  of  energy  which  would  result  from  loading  the  meter 
in  the  ordinary  way.  Also,  in  service  tests  after  the  meter 
has  been  installed  it  is  often  necessary  to  test  at  definite  loads 


Carbon     storage  Battery  4  V. 
Eheo. 

FIG.  287. — Connections  for  testing  a  watt-hour  meter  by  use  of  a  fictitious 

load. 

and  under  constant  conditions.  This  is  frequently  impossible 
if  the  customer's  load  is  relied  upon.  It  is  not  feasible  to  use 
large  rheostat  loading  boxes  on  account  of  their  expense  and  in- 
convenience. In  such  cases,  the  potential  and  current  circuits 
may  be  separately  excited  from  two  sources;  the  potential  cir- 
cuit from  the  line  as  usual  and  the  current  circuit  from  a  low- 
voltage  source. 

For  direct-current  work,  up  to  500  amp.,  two  Edison  stor- 
age cells  and  a  compact  carbon  rheostat,  as  indicated  in  Fig. 
.287,  are  very  convenient.  By  turning  back  the  handle  of  the 
rheostat,  the  circuit  is  broken  when  the  readings  are  not  being 
taken.  The  weight  of  the  cells  for  testing  500-amp.  meters  is 
about  180  Ib. 


ELECTRICITY  METERS 


501 


It  will  be  noticed  that  the  customer's  load  is  carried  by  the 
jumper,  which  is  put  on  before  the  meter  is  taken  out  of  service, 
thus  avoiding  any  interruption  of  the  circuit.  In  this  and  other 
cases  where  jumpers  are  used,  it  is  essential  that  they  be  so  applied 
that  the  normal  field  at  the  armature  of  the  meter  is  not  disturbed. 

For  tests  of  alternating-current  meters  after  installation,  it  is 
possible  by  the  use  of  a  special  step-down  transformer  connected 
across  the  mains,  to  obtain  large  fictitious  loads.  This  implies 
that  the  controlling  devices  may  be  made  simple  and  compact 
and  the  whole  apparatus  portable.  Such  devices  are  on  the 
market  and  are  sold  under  the  name  of  phantom  load  boxes. 
It  is  to  be  remembered  that  the  percentage  accuracy  of  an  alter- 
nating-current meter  depends  on  the  power  factor  of  its  load, 
so  it  is  necessary  to  be  sure  that  the  transformer  arrangement 
does  not  introduce  complications  due  to  phase  displacements. 

Phase -shifting  Devices. — In  testing  and  adjusting  alternating- 
current  meters  in  the  laboratory,  one  must  be  able  to  vary  the 


FIG.  288. — Diagram  for  phase -shifting  motor-generator  set. 

effective  power  factor  of  the  load,  preferably  without  any  at- 
tendant alteration  in  either  the  current,  voltage  or  wave  form. 
An  arrangement  for  this  purpose  is  shown  diagrammatically  in 
Fig.  288. 

It  consists  of  two  motor-driven  machines,  the  armatures  of 
which  are  rigidly  coupled;  one  field  is  stationary  while  the  other 
is  so  mounted  that  it  can  be  displaced  about  the  axis  of  the  shaft 
by  a  wormwheel  and  sector  and  its  angular  position  read  on 
a  graduated  arc.  The  displacement  may  be  effected  by  a  remote- 


502 


ELECTRICAL  MEASUREMENTS 


control  arrangement.  Machine  A  energizes  the  potential  coils 
of  the  meters  while  machine  B  supplies  the  current  coils;  B  is 
either  of  low  voltage  and  large  current  capacity  or  else  works 
through  a  step-down  transformer.  Both  machines  should  give 
sinusoidal  waves,  for  the  operation  of  induction  meters,  especially 


Phase  Shifting          . 
Transformer       Transfor.m.ej.s 


3  Phas 


FIG.  289. — Drysdale  phase-shifting  transformer. 

at  low  power  factors,  is  greatly  influenced  by  wave  form.  To 
obtain  good  wave  forms,  specially  designed  three-phase  machines 
with  Y-connected  armatures  are  necessary. 

A  much  simpler  and  less  expensive  device  for  accomplishing 


ELECTRICITY  METERS 


503 


the  same  purpose  is  the  Drysdale  phase-shifting  transformer,  the 
principle  of  which  is  explained  on  page  290. 

This  transformer  as  designed  for  meter  tests,  together  with  the 
connections  necessary  in  testing  three-phase  meters,  is  shown 
in  Fig.  289. 

The  phase-shifting  transformer  should  be  used  on  circuits 
which  have  sinusoidal  voltage  waves,  otherwise  the  wave  form  in 
the  secondary  will  change  with  the  adjustment  of  the  phase 
displacement. 

In  order  to  lag  an  induction  meter  it  is  necessary  to  operate 
it  at  two  power  factors  and  usually  1  and  0.5  are  chosen.  The 
double-motor  generator  set  or  the  phase-shifting  transformer 
previously  described  may  be  used,  but  these  two  particular 
power  factors  may  be  obtained  from  a  three-phase  circuit.  Fig. 
290  shows  the  connections. 


FIG.  290. — Arrangement  for  obtaining  power  factor  0.5  from  a  three-phase 

circuit. 

As  shown,  the  current  is  in  phase  with  #12,  the  voltage  at  the 
meters  in  phase  with  EiS  and  the  power  factor  is  0.5  leading. 
To  obtain  0.5  power  factor  with  lagging  current  the  voltage  coils 
would  be  connected  between  leads  3  and  2. 

To  determine  whether  one  is  dealing  with  a  lagging  or  leading 
current,  a  small  inductance,  L,  of  low  resistance,  may  be  included 
in  the  potential  circuit  of  the  standard  dynamometer  wattmeter; 
normally  this  inductance  is  short-circuited.  If  the  current  is  lag- 
ging, the  insertion  of  the  inductance  will  slightly  increase  the 
apparent  power  factor  and  will  decrease  it  when  the  current  is 
leading. 


504 


ELECTRICAL  MEASUREMENTS 


A  power  factor  of  zero  may  be  obtained  from  a  balanced  three- 
phase  circuit,  as  shown  in  Fig;.  291. 

The  currents  /i2  and  /i3  must  be  equal  and  the  resistances 
non-reactive. 

A  power  factor  of  zero  may  also  be  obtained  from  a  two-phase 
circuit,  the  voltage  being  taken  from  one  phase  and  the  current, 
through  a  non-reactive  resistance,  from  the  other.  It  must  be 
assured  at  the  beginning  that  the  two  phases  are  really  in  time 
quadrature  and  that  the  inductances  of  the  current  coils  .do  not 
cause  an  appreciable  phase  displacement.  Where  a  two-phase 


L=O 


FIG.    291. — Arrangement  for  obtaining  zero  power  factor  from  a 
three-phase  circuit. 

current  is  obtained  from  a  three-phase  circuit  by  Scott  trans- 
formers, unless  the  wave  forms  of  the  primary  supply  are 
sinusoidal,  the  wave  forms  in  the  secondaries  may  be  badly  dis- 
torted, one  being  flat-topped,  the  other  peaked. 

With  any  of  these  phase-shifting  devices  it  is  important  that 
the  voltage  and  current  waves  be  sinusoidal;  for  a  60°  displace- 
ment of  the  fundamental  in  the  current  wave  with  respect  to  the 
fundamental  in  the  voltage  wave  implies  a  180°  displacement  of 
the  third  harmonics,  a  300°  displacement  of  the  fifth  harmonics 
and  so  on.  A  statement  that  the  load  has  a  power  factor  of  0.5 
gives  little  idea  of  the  conditions  under  which  the  watt-hour 
meter  is  operating.  The  changed  phase  relation  greatly  compli- 
cates the  behavior  of  induction  meters. 

Testing  Polyphase  Induction  Meters. — When  a  single-phase 
induction  watt-hour  meter  is  used  on  a  non-inductive  load,  the 
error  due  to  incorrect  lagging  is  negligible.  If  a  polyphase  indue- 


ELECTRICITY  METERS 


505 


tion  watt-hour  meter  is  used  on  a  three-phase  load  of  power 
factor  unity,  the  error  due  to  incorrect  lagging  may  be  appre- 
ciable, for  in  this  case,  although  the  power  factor  of  the  load  is 
unity,  one  of  the  elements  of  the  meter  operates  at  a  power  fac- 
tor 0.866  leading  while  the  other  element  operates  at  a  power 
factor  0.866  lagging  (see  page  332). 

For  other  three-phase  power  factors  the  conditions  under  which 
the  elements  operate  are  shown  by  Fig.  294. 


FIG.  294. — Showing  the  power  factors  at  which  the  two  elements  of  a 
polyphase  watt-hour  meter  operate  when  the  balanced  three-phase  load  has 
different  power  factors. 

Suppose  the  upper  element  is  underlagged  while  the  lower  ele- 
ment is  overlagged.  Then,  when  the  upper  element  operates  at 
a  lagging  power  factor  and  the  lower  element  at  a  leading  power 
factor,  both  elements  tend  to  make  the  meter  register  too  little. 
If  the  elements  are  interchanged,  both  tend  to  make  the  meter 
register  too  high. 

Polyphase  induction  watt-hour  meters,  operated  through  in- 
strument transformers,  are  often  used  in  determinations  of  the 


506V  ELECTRICAL  MEASUREMENTS 

water  rates  of  three-phase  turbo-generators,  water  rheostat  loads 
being  employed.  The  three-phase  power  factor  is  then  unity. 
In  calibrating  the  meter,  together  with  the  transformers,  a  three- 
phase  non-inductive  load  should  be  used  and  the  connections  so 
made  that  the  element  which  operated  with  the  lagging  power 
factor  during  the  test  is  traversed  by  a  lagging  current  during 
calibration. 

Testing  of  Large  Direct-current  Watt-hour  Meters  on  Fluc- 
tuating Loads.15 — On  account  of  the  great  revenue  per  meter 
which  may  be  involved,  it  is  very  important  for  both  the  supply 
company  and  the  consumer  that  the  meters  by  which  large 
amounts  of  power  are  sold  be  kept  in  an  accurate  condition. 
The  necessary  tests  must  be  made  with  the  meters  in  place,  and 
if  they  are  used  on  a  rapidly  fluctuating  load,  such  as  a  street- 
railway  system,  difficulties  are  experienced  in  making  the  tests 
and  the  necessary  adjustments. 

Owing  to  the  large  number  of  readings  of  the  current  which 
it  is  necessary  to  take  in  order  to  obtain  a  good  average,  the  ordi- 
nary method  of  using  a  stop-watch  and  of  measuring  the  line 
voltage  and  current  is  a  time-consuming  operation,  and  in  some 
cases  the  fluctuations  are  so  rapid  that  the  use  of  the  ammeter 
is  quite  out  of  the  question.  An  alternative  procedure  is  to  take 
the  meter  out  of  service  and  to  send  through  its  coils  the  current 
from  a  storage  battery  (see  page  500).  This  current  may  be 
controlled  by  resistors,  so  that  tests  at  light  load  and  up  to  about 
500-amp.  may  be  made  without  the  apparatus  being  too  un- 
wieldy to  be  managed  by  two  persons.  For  this  purpose  two 
Edison  cells  are  convenient,  being  readily  portable.  It  is,  how- 
ever, desirable  to  avoid  taking  the  meter  out  of  service,  for  the 
test  may  occupy  an  hour  or  more,  and  the  loss  of  revenue  is  worth 
obviating;  it  may  be  as  much  as  $5  to  $10  for  each  hour  the  meter 
is  out  of  service.  Also  it  is  desirable  to  make  the  test  with  the 
customer's  regular  load. 

The  very  convenient  portable  standard  watt-hour  meters  de- 
veloped for  alternating-current  work  naturally  suggested  similar 
devices  for  use  on  direct-current  circuits.  Their  development, 
however,  has  been  attended  with  much  difficulty.  Nevertheless 
the  problem  has  been  solved  quite  successfully,  and  the  best  of 
these  instruments,  when  carefully  used,  are  of  great  service  where 


ELECTRICITY  METERS 


507 


load  conditions  are  extremely  variable.  Such  test  meters  are 
now  made  in  capacities  up  to  150  amperes. 

In  railway  work,  it  is  frequently  necessary  to  test  meters  of 
several  thousand  amperes  capacity.  The  direct  application  of 
shunts  to  a  portable  standard  watt-hour  meter,  of  the  commuta- 
ting  type,  is  not  permissible  on  account  of  the  change  of  the  multi- 
plying power  of  the. shunt  through  heating,  and  the  uncertainty 
due  to  bad  contacts. 

As  it  is  desirable  to  retain  this  type  of  meter  as  a  standard, 
methods  have  been  devised  whereby  shunts  are  applied  to  the 
portable  standard  watt-hour  meter  in  such  a  way  that  errors  due 
to  heating  and  to  contact  resistances  are  eliminated. 


FIG.  295. — Showing  connections  for  testing  large  direct-current  watt-hour 
meters  by  the  differential  multiplier  method. 

One  method  is  shown  in  Fig.  295,  where  for  the  sake  of  sim- 
plicity the  potential  connections  to  the  meters  are  omitted.  The 
arrangement  may  be  called  a  differential  multiplier,  for  by  its  use 
the  range  of  the  portable  standard  watt-hour  meter  is  extended. 

The  station  busbar  is  arranged  so  that  it  has  a  narrow  gap'  at  G. 
This  gap  is  ordinarily  closed  by  plates  firmly  bolted  in  position. 
The  gap  should  be  narrow  and  the  leads  so  arranged  that  the  field 
at  the  meter  is  not  altered  when  the  gap  is  opened.  The  test 
circuit  is  clamped  to  the  bus  bars  and  the  gap  opened  without  in- 
terrupting the  service.  The  entire  current  then  flows  to  a,  where 
it  divides,  a  comparatively  small  portion  flowing  through  the  fine 
wire  coils  of  the  multiplier  MM',  the  rotary  standard  and  the 


508 


ELECTRICAL  MEASUREMENTS 


adjustable  resistor  r,  to  b.  The  main  portion  flows  through  the 
" coarse  coil"  C  of  the  multiplier,  which  is  in  this  case  a  straight 
bar,  then  through  the  resistor  R,  which  is  of  such  a  magnitude  as 
to  give  the  voltage  drop  required  in  the  standard  meter  circuit. 
The  fields  due  to  the  currents  in  MM'  and  C  are  opposed,  and  in 
the  resultant  field  is  placed  an  astatic  movable-coil  system,  which 
is  provided  with  pivots  and  a  damping  device.  The  movable 
member,  in  series  with  a  suitable  resistor,  is  placed  across  the  line, 
and  serves  to  show  when  the  fields  due  to  C  and  MM'  are  bal- 
anced. The  adjustment  is  made  by  varying  r.  The  ratio  of  the 

currents  y1  =  K,  which  is  necessary  for  a  balance,  is  determined  in 

12 

the  laboratory,  therefore  the  corrected  watt-hours  by  the  test 
meter  are  obtained  by  multiplying  its  indications  by  K  +  1. 

The  standard  meter  is  set  up  where  it  will  be  as  free  from  stray 
fields  as  possible.     The  leads  to  it  are  flexible  and  readings  are 


Diff.M.V. 

FIG.  296. — Arrangement  for  testing  large  direct-current  watt-hour  meters 
by  use  of  two  shunts  and  a  differential  millivoltmeter. 

taken  with  the  meter  in  four  different  azimuths  90°  apart.  This 
is  usually  sufficient;  but  conditions  may  arise  where,  owing  to 
the  change  in  the  distribution  of  current  between  feeders  which 
are  at  different  distances  from  the  test  meter,  this  procedure 
would  not  eliminate  the  stray  field  errors.  In  such  cases,  a 
shielded  instrument  is  desirable.  The  multiplier  being  astatic, 
with  the  centers  of  the  upper  and  lower  coils  2.5  in.  apart,  is 
not  affected  by  uniform  stray  fields.  Anything  that  produces  a 
non-uniform  stray  field — for  instance,  a  busbar  close  to  the  in- 
strument— might,  however,  lead  to  a  misinterpretation  of  the 
balance.  So  the  apparatus  should  be  set  up  at  some  distance 
from  the  switchboard.  Fig.  296  shows  a  method  where  the 


ELECTRICITY  METERS 


509 


balance  is  not  affected  by  stray  fields.  Two  resistors,  one  in  the 
circuit  of  the  test  meter,  and  the  other  in  the  parallel  circuit,  are 
employed.  The  potential  drops  in  the  two  are  made  equal  by 
the  adjustable  resistor  r  and  this  equality  is  indicated  by  a  differ- 
ential millivoltmeter  of  the  D'Arsonval  pattern.  Any  shunts 
which  are  suited  to  the  purpose  may  be  temporarily  bolted 
together  and  used  for  Si  and  $2.  They  should  be  free  from  ther- 
mal errors  as  these  are  troublesome  in  some  cases. 

The  arrangement  may  be  simplified  and  the  differential  milli- 
voltmeter replaced  by  a  pivoted  D'Arsonval  galvanometer  if  a 
special  double  shunt  be  constructed  for  the  purpose.  The  con- 
nections are  shown  in  Fig.  297.  Inspection  of  the  figure  will 


FIG.  297. — Connections  for  testing  large  direct-current  watt-hour  meters 
by  the  bridge  method. 

show  that  the  arrangement  has  become  a  Wheatstone  bridge,  the 
low-resistance  sides  being  composed  of  fixed  resistors.  One  of 
the  high-resistance  sides  is  a  resistor  of  fixed  value;  the  other  is 
made  up  of  the  rotary  standard  and  the  necessary  adjustable 
resistor  for  maintaining  the  bridge  in  balance  when  contact  and 
coil  resistances  change.  The  sections  of  the  shunt  (see  Fig.  298) 
Si  and  $2  have  a  common  terminal  at  a.  If  the  galvanometer 

T  (^ 

stands  at  zero,  then  j-  =  0  ,  and  the  corrected  reading  of  the 

^2  01 

test  meter  is  its  indication  multiplied  by  -—j- — 2.     By  the  use  of 

12 


510 


ELECTRICAL  MEASUREMENTS 


FIG.  298. — Special  double  shunt  for  use  in  bridge  method  of  testing  large 
direct-current  watt-hour  meters. 


Kot.Std. 


Arrangement  of  Shunts 

and  Besistances  for  Testing 

1000  Ampere  Meters 


To  Load 


Rot.Std. 


To  Load 


From  Meter 

Arrangemene  of  Shunts 

and  Eesistances  for  Testing 

MOO  Ampere  Meters 


FIG.  299. — Double  shunt  and  fixed  resistances  for  use  in  bridge  method  of 
testing  large  direct- current  watt-hour  meters. 


ELECTRICITY  METERS  511 

two  potentiometers  to  measure  I\  +  1 2  and  72  when  the  galva- 
nometer is  balanced,  the  multiplying  factor  can  be  very  accurately 
determined  in  the  laboratory. 

In  a  particular  case  the  capacity  of  the  test  meter  used  is  40 
amp.  and  there  are  two  sets  of  shunts  and  auxiliary  resistances,  R, 
mounted  on  the  same  base,  the  ratings  being  1,000  amp.  and  2,000 
amp.  (see  Fig.  299).  The  voltage  drop  in  the  shunts  at  full  load 
is  100  millivolts,  and  in  the  resistor  R  it  is  400  millivolts.  The 
adjustable  resistor,  r,  is  a  strip  of  Boker  metal,  the  effective  length 
of  which  can  be  altered  by  the  use  of  screw  clamps.  To  obtain  a 
fine  adjustment  a  carbon  compression  rheostat  is  placed  in  paral- 
lel with  the  strip. 

DEMAND  INDICATORS 

The  business  of  supplying  electrical  energy  is  peculiar  because, 
broadly  speaking,  the  product  to  be  sold  cannot  be  stored.  It 
must  be  used  as  generated  and  the  supply  company  must  stand 
ready  to  furnish  its  product  to  customers  at  any  hour. 

The  demand  of  the  individual  consumer  for  the  company's 
product  passes  through  a  fairly  well-defined  daily  and  seasonal 
variation,  naturally  being  the  greatest  when  the  days  are  the 
shortest.  It  is  necessary  to  install  generating  machinery  of  suf- 
ficient capacity  to  carry  safely  the  greatest  aggregate  demand, 
or  the  peak  of  the  load  as  it  is  called,  and  provide  a  sufficient 
reserve.  This  means  that  machinery,  representing  a  consider- 
able investment,  must  stand  idle  for  a  larger  portion  of  the  time. 
This  peculiarity  of  the  business  has  led  electrical  companies  to 
divide  the  cost  of  supplying  their  consumers  into  two  parts, 
"  fixed  costs,"  which  are  independent  of  the  amount  of  the  prod- 
uct delivered  to  the  consumer,  and  " running  costs,"  which 
•  depend  directly  upon  the  amount  of  energy  delivered. 

On  account  of  the  large  amount  of  time  during  which  a  por- 
tion of  the  machinery  and  the  distribution  system  is  idle,  the 
" fixed  costs"  are  large  and  efforts  have  been  made  to  establish 
systems  of  rates  which  are  in  accordance  with  Hopkinson's 
maxim  that  "the  charge  for  a  service  rendered  should  bear  some 
relation  to  the  cost  of  rendering  it." 

The  investment  necessary  in  order  that  a  company  may  stand 
ready  to  supply  any  group  of  consumers  is  dependent  on  the 


512  ELECTRICAL  MEASUREMENTS 

maximum  demand  which  the  consumers  make  for  the  com- 
pany's product,  and  in  certain  systems  of  charging,  maximum- 
demand  indicators  are  used  in  conjunction  with  the  watt-hour 
meters  as  an  aid  in  apportioning  the  fixed  costs  among  the 
consumers. 

Demand  indicators  record  the  greatest  sustained  amount  of 
current,  or  power,  which  the  consumer  uses.  They  are  not 
supposed  to  indicate  demands  which  are  of  such  short  duration 
that  no  serious  burden  is  placed  thereby  on  the  generating 
machinery.  The  length  of  time  during  which  the  demand  must 
be  sustained  in  order  that  the  indicator  may  register  depends 
upon  the  character  of  the  service;  for  power  work  some  com- 
panies use  a  J^-hr.  period,  but  a  5-min.  period  is  not  uncommon, 
especially  with  badly  fluctuating  loads. 

Strictly  speaking,  to  furnish  adequate  data  for  use  in  deter- 
mining rates,  a  demand  indicator  should  give  not  only  the  demand 
but  the  hour  at  which  it  occurs;  for  a  consumer  who  takes  a 
large  demand  at  a  time  when  the  generating  machinery  and  dis- 
tribution system  would  otherwise  be  idle  necessitates  no  addi- 
tional investment  and  can  be  given  a  better  rate  than  a  con- 
sumer who  makes  the  same  demand  at  the  time  of  peak  load. 
It  is  only  in  the  case  of  large  consumers  that  a  supply  company 
is  justified  in  installing  an  expensive  form  of  demand  indicator 
which  will  show  the  time  at  which  the  maximum  demand  occurs 
as  well  as  its  magnitude. 

With  small  consumers,  instruments  such  as  the  Wright  or 
the  General  Electric  Co.  M-2  demand  meters  are  used  and  the 
allowance  for  the  fact  that  all  the  demands  do  not  occur  simul- 
taneously is  made,  by  use  of  the  diversity  factor,  when  the  rates 
are  originally  determined.  The  diversity  factor  is  defined  as  the 
ratio  of  the  sum  of  the  maximum  power  demands  of  the  subdi- 
visions of  any  system  or  part  of  a  system  to  the  maximum  de- 
mand of  the  whole  system  or  of  the  part  of  the  system  under 
consideration,  measured  at  the  point  of  supply. 

Diversity  factors  can  be  determined  only  by  actual  observa- 
tion of  the  consumers'  maximum  demands  and  the  corresponding 
maximum  demand  on  the  station.  They  will  be  different  for 
different  classes  of  service. 

In  consequence  of  the  detailed  study  of  electrical  rates  now 


ELECTRICITY  METERS 


513 


being  carried  on,  the  demand  indicator  is  an  instrument  of  in- 
creasing importance  and  is  being  rapidly  developed. 

The  Wright  Maximum-demand  Indicator.13 — This  indicator, 
which  was  the  first  maximum-demand  instrument,  may  be  looked 
upon  as  a  registering  differential  thermometer,  one  bulb  of  which 


FIG.  300. — Wright  demand  indicator. 

is  heated  by  the  passage  of  the  current  through  a  suitable  heater 
coil  which  closely  surrounds  it.  It  registers  the  maximum  current. 

The  internal  appearance  of  the  indicator  as  made  in  the  smaller 
sizes,  up  to  and  including  25  amp.,  is  shown  in  Fig.  300. 

The  essential  working  parts  are  the  indicator  tube,  with  its 
attached  index  tube  i2,  the  scale  s,  and  the  heater  strips  C. 

33 


514  ELECTRICAL  MEASUREMENTS 

In  the  small  sizes  (up  to  and  including  25  amp.)  the  cus- 
tomer's entire  current  is  ataken  in  through  the  leads,  LL,  and  to 
the  heater  strips  via  the  spring  hinges,  h,  and  flexible  connecting 
strips,  k. 

The  indicator  tube  is  of  glass,  annealed  so  that  it  will  bear 
handling  and  not  be  subject  to  changes  due  to  stresses  in  the  glass; 
the  two  bulbs,  hi  and  62,  which  are  nearly  equal  in  volume,  con- 
tain air.  The  U-tube  connecting  them  contains  concentrated 
sulphuric  acid  in  such  an  amount  and  so  adjusted  in  the. tube 
that  when  the  indicator  is  cold  and  set  ready  to  begin  to  operate, 
the  level  of  the  liquid  is  at  d,  so  that  it  is  just  on  the  point  of  flow- 
ing into  the  index  tube,  ^2.  Sulphuric  acid  is  used  because  it 
"wets"  the  glass,  is  very  heavy,  flows  readily,  is  hygroscopic, 
and  expands  comparatively  little  with  rise  of  temperature.  To 
prevent  accidental  transfer  of  air  from  bi  to  62,  or  vice  versa, 
especially  when  the  indicator  is  set,  the  tube  is  constricted  to  a 
capillary  at  g  and  g'  and  two  traps  are  provided  at  t  and  t' '. 

The  heater  strips  are  of  an  alloy  of  high  resistivity,  which  is 
but  little  affected  by  temperature;  the  strips  are  of  very  thin 
metal  and  are  made  to  embrace  closely  the  cylindrical  glass 
bulb,  61,  by  means  of  screw  clamps.  In  the  small-sized  indica- 
tors, where  it  is  necessary  to  carry  the  heater  strips  around  the 
bulb  a  number  of  times,  a  non-inductive  form  is  used.  The 
object  of  this  construction  is  to  prevent  the  turns  drawing  to- 
gether when  a  short-circuit  occurs ;  if  this  should  happen  the  strips 
would  very  likely  be  burned  out  or  their  intimacy  of  contact 
with  the  glass  so  altered  that  an  error  would  be  introduced.  The 
corrugated  copper  terminals  form  somewhat  flexible  electrical 
connections  to  the  heater  proper.  In  indicators  having  a  range 
of  35  amp.  and  above,  shunts  are  used,  the  heater  strips  being  of 
the  15-amp.  type.  In  the  shunted  instrument,  to  insure  per- 
manency of  calibration,  it  is  essential  that  all  the  electrical 
joints  be  soldered. 

The  indicator  is  set  by  raising  the  lower  end  of  the  tube  board, 
M,  on  which  the  above  described  members  are  mounted,  until 
it  is  somewhat  above  the  spring  hinges,  h,  on  which  it  is  pivoted. 
This  allows  the  liquid  in  the  index  tube  iz  to  drain  back  into  the 
U-tube;  when  thoroughly  drained  and  the  board  is  lowered  to  its 
normal  position,  the  U-tube  is  filled  with  liquid  up  to  d. 


ELECTRICITY  METERS 


515 


If  a  current  is  now  sent  through  the  heater  strips,  the  air  in  b\  is 
heated  and  expands,  causing  the  liquid  to  flow  slowly  into  the 
index  tube  i%  which  is  in  front  of  the  graduated  scale;  the  flow 
will  continue  until  the  permanent  state  of  temperature  corre- 
sponding to  that  particular  current  is  reached. 

Owing  to  the  heat  capacity  of  the  strips,  the  glass  bulb,  etc., 
and  the  poor  thermal  conductivity  of  the  glass,  the  response  of  the 
indicator  to  the  increase  of  current  is  sluggish;  this  lag  of  the 
reading  behind  the  increase  of  current  is  essential  to  the  success- 
ful operation  of  any  such  device,  for  it  must  not  take  cognizance 


s  n 


85  %  of  Final  Beading 


13.5  Ampsl 


10  Amps 


6.5  Amps. 


35  j(   of  Final  Reading 


0     5     10    15    20    25    30    35    40    45    50    55   GO 
Time  in  Minutes 


FIG.  301. — Showing  characteristics  of  Wright  demand  indicator. 


of  currents  which  last  for  only  a  very  short  time.  The  indication 
desired  is  that  due  to  the  sustained  maximum.  Fig.  301  shows 
this  gradual  increase  of  reading  when  the  current  is  kept  constant. 
It  is  intended  that  approximately  90  per  cent,  of  the  full-load 
registration  be  accomplished  in  4  min.  and  the  entire  registra- 
tion in  about  40  min. 

It  will  be  noted  from  Fig.  301  that  the  rise  to  a  fair  approxima- 
tion  to  the  final  reading,  say  85  per  cent  of  it,  occurs  more 
abruptly  when  the  indicator  is  worked  at  about  its  full  capacity 
than  when  it  is  lightly  loaded.     Fig.  302  illustrates  this  point;  a 
'  50-  and  a  100-amp,  indicator  were  tested  in  series  at  45  amp.     Of 


516 


ELECTRICAL  MEASUREMENTS 


course,  each  indicator  has  its  characteristic  rate  of  response  to  the 
current. 

Another  point  may  be  noted :  after  the  device  has  cooled  down, 
owing  to  shutting  off  the  current,  there  will  be  no  increase  of 
reading  when  a  current  slightly  larger  than  that  previously  reg- 
istered, is  turned  on  until  the  larger  current  has  been  maintained 
for  a  time  longer  than  the  normal  time  lag  of  the  indicator;  for 
that  time  must  elapse  before  there  has  been  sufficient  expansion 
of  the  air  in  61  to  cause  the  liquid  again  to  begin  to  flow  into  the 


100 


5    10    15  20  25  30  35  40    45  50  55    60 
Time  in  Minnies 

FIG.  302. — Illustrating  the  influ- 
ence of  the  size  of  a  Wright-demand 
indicator  on  the  rate  at  which  the 
final  reading  corresponding  to  a 
given  current  is  attained. 


— 

u°" 

rve 

B 

1C 

.5  , 

im 

ps. 

13 

\ 

a  9  

/ 

ii 

A 

np 

, 

*    1 

a  8        1 

K 

•     / 

Cu 

rve 

A 

1  44 

o  sU- 

r?  i   I 

i  4|F 

*    of 

« 

°0     5    10  15   20  25   30  35   4Q  45   50  55  60 
Time  in  Minutes 

FIG.  303.— Showing  the  delay  of 
a  Wright-demand  indicator  in  be- 
ginning registration  after  the  indi- 
cator has  cooled  down. 


index  tube.  This  is  illustrated  in  Fig.  303.  Curve  A  shows  the 
normal  rise  of  the  indication,  when,  after  the  device  has  been  set, 
the  current  is  maintained  at  10  amp.  After  the  current  had  been 
cut  off  and  the  indicator  allowed  to  cool  thoroughly,  a  run  at 
10.5  amp.  gave  curve  B,  the  indicator  not  being  reset. 

Owing  to  differences  in  the  tubes,  it  is  impracticable  to  print 
the  scales,  for  each  must  be  graduated  by  experiment  to  fit  the 
particular  tube  to  which  it  is  applied.  It  is  usual  to  determine 
either  four  or  five  points  by  passing  measured  currents  through 
the  indicator  for  a  sufficient  time,  and  marking  on  the  scale  the 
corresponding  heights  of  the  liquid  in  the  index  tube  z'2;  the 


ELECTRICITY  METERS 


517 


subdivision  is  done  mechanically.  The  20  per  cent  load  mark  is 
the  lowest  one  on  the  scale. 

The  readings  at  the  lower  end  of  the  scale  are  considerably 
influenced  by  temperature.  The  effect  of  temperature  becomes 
smaller  as  the  readings  increase.  This  is  illustrated  by  the  fol- 
lowing tests:  Two  indicators,  one  of  5,  the  other  of  10  amp. 
capacity,  were  used.  They  were  placed  in  a  suitable  chamber  in 
which  were  heating  coils  and  a  fan  to  circulate  the  air.  The  tem- 
perature being  originally  at  68°F.  was  raised  to  104°F.,  no  cur- 
rent being  sent  through  the  indicators.  The  rise  of  liquid  in  the 
index  tube  was  for  the  5-amp.  indicator  0.38  in.,  for  the  10-amp. 
indicator  0.50  in. 

The  temperature  was  maintained  constant  for  4  hr.  at  104°F., 
the  fan  being  kept  running;  at  the  end  of  this  time  the  20  per 
cent,  load  test  was  begun;  the  other  tests  followed  as  usual,  and 


150 
140 

•|l20 

I100 
«  80 

1    60 
o 

1   4° 
20 

0 

^ 

104" 

F. 

• 

"<- 

.__ 

08 

9? 

D     10     20    30     40     50     60     70    80     90  1Q 

15U 

§1"0 

\ 

104 
I 

F. 

2 
.-SlOO 

3  so 
Joo 

!« 

2) 

0 

^~~ 





—  . 



68 

F. 

3  10  20  30  40  50  CO  70  80  3D  1(X 

Per  Cent  aC  Full  Load 


Per  Cent  at  Full  Load 


FIG.  304. — Illustrating  the  effect  of  temperature  on  two  Wright  demand 

indicators. 

the  results  are  shown  in  Fig.  304.  It  will  be  seen  that  the  low 
readings  are  very  considerably  affected,  that  the  percentage  error 
decreases  with  an  increase  of  load,  and  that  each  instrument  has 
its  own  characteristic  behavior. 

The  leads  to  the  indicator  influence  its  action  by  conducting 
heat  away  from  the  bulb ;  the  error  so  introduced  will  depend  on 
the  size  of  the  leads  and  the  difference  in  temperature  between 
the  heater  strip  and  the  outside  air. 

In  a  two- wire  service  one  indicator  is  installed  on  the  customer's 
side  of  the  watt-hour  meter.  According  to  American  practice  it 
is  customary  in  a  three- wire  service  to  install  two  indicators,  one 


518 


ELECTRICAL  MEASUREMENTS 


on  each  side  of  the  circuit;  in  this  case  the  average  of  the  two 
readings  is  used.  Obviously  there  is  no  guarantee  that  the  two 
maxima  occur  simultaneously.  The  cheapness  of  the  Wright 
demand  indicator  permits  its  use  with  the  small  consumer.  In 
practice,  immediately  after  the  reading  of  the  instrument  has 
been  taken,  it  is  reset  by  the  reader  employed  by  the  supply 
company.  No  trace  of  the  indication  remains,  and  no  opportun- 
ity exists  for  its  subsequent  verification  in  case  of  a  dispute. 

General  Electric  Type  W  Watt  Demand  Indicator.— This 
device  is  made  for  use  on  alternating-current  circuits  and  for 
polyphase  work  only;  it  is  essentially  a  polyphase  indicating  watt- 
meter of  the  induction  type,  which  is  provided  with  an  exceed- 
ingly strong  electromagnetic  damping  system,  so  that  its  response 
to  variations  of  the  load  is  rendered  very  slow.  The  indications 

are  given  on  a  dial  which  is 
provided  with  two  pointers,  one 
of  which  indicates  the  load  (sub- 
ject to  the  time  lag  of  the  in- 
strument); the  other  shows  the 
sustained  maximum  to  which  the 
load  has  risen.  Fig.  305  shows, 
in  diagram,  the  essential  features 
of  the  instrument.  Wi  and  TF2 
are  the  two  wattmeter  elements 
which  are  essential  to  the  meas- 
urement of  power  in  the  ordi- 
nary polyphase  systems,  for,  as 
is  usual  in  such  measurements, 
the  " two-wattmeter  method"  is 
here  employed;  DI  is  the  disc  in 
which  currents  are  induced  by  the  elements  W\  and  W-z;  these 
currents  react  with  the  magnetic  fields  set  up  by  W\  and  Wi  and 
cause  the  indication  of  the  instrument.  The  disc  is  made  of  brass 
in  order  that  the  effect  of  temperature  changes  may  be  minimized, 
since  the  electrical  resistance  of  alloys  like  brass  varies  much  less 
with  changes  of  temperature  than  does  that  of  pure  metals,  such 
as  copper. 

The  controlling  spring  against  which  the  movable  system  de- 
flects is  at  S.  In  reality  three  springs  are  used  in  series  in  order 


M 


M     M 


FIG.  305. — Diagram  for  General 
Electric  type  W  watt  demand 
indicator. 


ELECTRICITY  METERS 


519 


that  the  movable  system  may  be  enabled  to  make  three  complete 
revolutions  without  complications  arising  from  the  spring  being 
twisted  too  tightly. 

The  damping  disc  D2  is  of  copper  and  rotates  between  two 
sets  of  magnets  M  and  Mf.  Each  magnet  is  adjustable  vertic- 
ally, so  that  the  strengths  of  the  magnetic  fields  through  which  the 
disc  moves  may  be  varied.  In  this  manner  the  strengths  of  the 
currents  induced  in  the  disc  when  it  turns,  and  consequently  the 
retardation  experienced  by  it,  may  be  altered  and  the  rapidity 
with  which  the  instrument  responds  to  changes  of  load  adjusted. 
It  is  intended  that  the  magnets  be  so  set  that  with  a  constant 
load,  90  per  cent,  of  the  registration  is  produced  in  5  consecutive 
minutes. 

The  hand  HI  is  driven  from  the  spindle  by  a  system  of  gear- 
ing, and  moves  over  a  dial  graduated  in  kilowatts.  As  it  moves 


10  15 

Time  in  Minutes 

FIG.  306. — Characteristic  of  General  Electric  type  W  demand  indicator. 

it  pushes  before  it  the  hand  H2,  which  is  loose  on  the  shaft  and 
provided  with  a  ratchet  R  and  a' light  spring  S',  which  tends  to 
turn  the  hand  back  against  the  ratchet.-  The  result  is  that  H2 
is  pushed  up  to  the  maximum  by  H  i  and  left  there,  when,  owing 
to  the  decrease  of  the  load,  HI  returns  toward  zero.  The  instru- 
ment may  be  set  by  opening  the  case  and  raising  the  ratchet 
which  allows  S'  to  return  the  pointer  Hz  to  zero,  H  i  being  pre- 
viously turned  back  to  that  point.  It  will  be  seen  that  this  de- 
vice gives  the  power  which  is  being  used  at  any  time,  as  well  as 


520 


ELECTRICAL  MEASUREMENTS 


the  maximum  demand  in  kilowatts.     It  gives  no  indication  of 
the  time  when  the  maximum  occurred. 

Though  the  principle  on  which  it  works  is  entirely  different, 
this  instrument  is  purposely  designed  to  have  the  same  general 
operating  characteristics  as  the  Wright  demand  indicator.  This 
will  be  seen  by  reference  to  Fig.  306,  which  shows  the  motion  of 
the  pointer  from  its  zero  position  after  turning  on  the  current. 


FIG.  307. — Ingalls  relay  demand  indicator. 

Ingalls  Relay  Demand  Indicator.13 — This  device  may  be  re- 
garded as  an  auxiliary  to  the  watt-hour  meter  by  means  of  which 
the  number  of  revolutions  made  by  that  instrument  in  a  given 
time  (half  an  hour)  may  be  obtained  from  a  record  impressed 
on  a  uniformly  moving  paper  tape.  From  this  record,  knowing 


ELECTRICITY  METERS  521 

the  disc  constant  of  the  watt-hour  meter  and  the  gear  ratio  of 
the  contact  arrangement  which  is  described  later,  the  demand 
may  be  calculated. 

Fig.  307  shows  the  general  appearance  of  one  of  these  devices. 
A  very  powerful,  double-spring  clock  or  an  electrically  driven 
clock  is  used  to  drive  the  drum  D  over  which  the  paper  tape  T 
is  passed ;  to  prevent  slipping  of  the  tape  the  drum  is  armed  with 
needle  points.  By  the  clockwork  the  tape  is  drawn  from  the 
magazine  M  and  caused  to  pass  in  front  of  the  punch  P.  W  is 
the  take-up  roll  and  is  actuated  by  a  friction  drive  from  the  clock. 
M'  is  the  magazine  roll  for  the  strip  of  carbon  paper  used  in 
impressing  the  record  on  the  tape. 

Whenever  a  current  is  passed  through  one  of  the  magnets  of 
the  punch  P  the  corresponding  armature  is  drawn  in  and  a 
mark  is  made.  Once  each  hour  a  reference  mark  is  printed  on 
the  tape. 

To  actuate  the  punch  a  contact  arrangement  is  added  to  the 
counter  of  the  watt-hour  meter;  it  is  shown  diagrammatically  in 
Fig.  308.  The  wheel  g  is  driven  by  /  r~i 

the  counter  and  revolves  once  for  each 
100  revolutions  of  the  meter  disc. 
The  contactor  C  and  the  weight  W 
are  in  one  piece,  which  is  loose  on  the 
shaft.  The  pin  P  is  long  enough  to 
engage  with  this  piece  and  then  to 
push  it  to  the  dotted  position,  when 
it  suddenly  falls  forward.  This  causes  FIG.  308. — Diagram  of 
the  contactor  C  to  connect  b  and  b'  contacts  for  Ingalls  relay 
,.  .  ,..»..  demand  indicator, 

for  an  instant,  thus  closing  the  circuit 

through  the  magnets  of  the  punch,  which  then  marks  the  tape. 
After  100  revolutions  of  the  meter  disc  this  operation  is  repeated. 
The  appearance  of  the  record  thus  obtained  is  seen  in  Fig.  309. 

The  tapes  are  replaced  once  a  week;  when  this  is  done  the  time 
of  the  beginning  and  the  ending  of  the  record  is  recorded  on  the 
tape. 

To  find  the  maximum  demand  the  tape  is  examined  and  those 
parts  where  the  marks  appear  to  be  closest  together  are  selected 
for  measurement.  A  scale  having  a  length  corresponding  to  the 
movement  of  the  tape  during  ^  hour  is  applied,  and  the  number 


522  ELECTRICAL  MEASUREMENTS 

of  spaces  in  this  length  is  determined.  Each  one  of  the  spaces 
corresponds  to  100  revolutions.  Thus  the  maximum  number  of 
revolutions  made  by  the  watt-hour  meter  in  J^  hour  is  found. 
The  ordinary  formula  for  the  watt-hour  meter  is 

NXKX  3,600 

~tx 1,000  — ' 

where  N  is  the  number  of  revolutions  of  the  meter  disc  occurring 
in  t  sec.  and  K  is  the  disc  constant  of  the  meter.  The  kilowatts 
demand  corresponding  to  one  space  on  the  paper  tape,  that  is, 
to  100  revolutions,  if  they  occurred  in  J^  hour  would  then  be 

100  X  K  X  3,600 
30  X~60  X  1,000 

If  instead  of  one  space  in  J^-hour,  there  be- any  other  number, 
the  above  is  simply  multiplied  by  the  number  of  spaces.     To 


FIG.  309. — Record  from  Ingalls  relay  demand  indicator. 

illustrate :  take  the  tape  shown  in  Fig.  309  and  assume  that  the 
disc  constant,  K,  of  the  watt-hour  meter  is  25.  Then  the  kilo- 
watts demand  is  given  by  0.2  X  25  X  (maximum  number  of 
spaces  in  ^  hour). 

Where  the  marks  are  closest  together  there  are  eight  spaces  in 
^  hour,  so  the  demand  is 

0.2  X  25  X  8.0  =  40  kw. 

It  will  be  noticed  that  the  device  gives  information  of  value 
other  than  the  maximum  demand,  for  it  tells  just  how  the  cus- 
tomer's load  varies  and  gives  the  hour  at  which  the  maximum 
demand  is  reached.  This  may  or  may  not  be  at  the  time  of  the 
peak  of  the  load  on  the  station. 

The  accuracy  of  this  device  depends:  first,  on  the  accuracy  of 
the  watt-hour  meter  to  which  it  is  applied;  second,  on  the  rate 
of  the  clock  mechanism. 


ELECTRICITY  METERS 


523 


The  General  Electric  M-2  Demand  Indicator. — Fig.  310  shows 
the  M-2  demand  indicator  made  by  the  General  Electric  Co.  for 


Operating  Coil 


Armature 


FIG.  310. '—  General  Electric  Co.  M-2  demand  indicator. 

use  in  conjunction  with  a  watt-hour-meter.     Referring  to  the 
diagram,  which  is  for  the  instrument  used  on  alternating-current 


524  ELECTRICAL  MEASUREMENTS 

circuits,  a  contact  on  the  registering  train  of  the  watt-hour 
meter  closes  the  circuit  of  the  operating  coil  every  time  the 
registration  of  a  definite  number  of  kilowatt-hours  has  been 
completed.  When  the  armature  is  attracted,  the  dog  is  advanced 
by  the  ratchet  and  pushes  the  friction  pointer  before  it. 

To  introduce  the  time  element,  the  clutch  (a  sliding  gear)  is 
controlled  by  the  trip  levers  which  in  turn  are  controlled  by  a 
cam  arrangement  driven  through  a  system  of  gearing  from  a 
constant-speed  motor.  The  trip  levers  are  thus  operated  period- 
ically, every  half  hour  for  instance,  and  the  clutch  thrown  out  of 
gear,  allowing  the  spiral  spring  to  return  the  dog  to  the  beginning 
of  its  traverse.  The  friction  pointer  will  thus  be  left  at  the  end 


FIG.  311. — Record  from  General  Electric  registering  demand  indicator. 

of  the  largest  traverse  of  the  dog  and  will  indicate  the  maximum 
demand.  Arrangements  are  made  for  regulating  the  speed  of 
the  motor  in  order  that  the  time  element  may  be  adjusted. 

When  the  indicator  is  used  on  a  direct-current  circuit  the 
clutch  i^  operated  by  an  8-day  clock. 

The  General  Electric  Co.  also  manufactures  a  registering 
demand  indicator  which  is  based  upon  the  same  principle.  An 
arm,  corresponding  to  the  friction  pointer,  carries  a  stylus  which 
draws  lines  on  a  circular  chart  which  are  proportional,  when 
properly  scaled,  to  the  demand  during  the  consecutive  30-min. 
or  other  period  for  which  the  indicator  is  set.  Fig.  311  shows 
such  a  record. 


ELECTRICITY  METERS 


525 


Printometer. — This  is  a  device  to  be  used  in  connection  with 
watt-hour  meters.     It  prints  on  a  paper  tape  the  equivalent  of 


Meter  Dial 


Supply 


Meter 
Contact 


Watt-hour 
1  Meter  Spindle 

20 

—  —  •  —  ~_ 

159 

F-C—  , 

21 

165 

]  ^SD 

22 

168 

^^==^> 

23 

173 

j 

24 

178 

1 

184 

illation 

2 

189 

al 

3 

193 

breaking  Device 

4 

193 

need  One  Point 

5 

197 

Meter  Begister. 

G 

202 

of  Type  Wheels 
Time  Interval. 

7 

207 

J- 

J10 

Printing  Plate 

Eaised  when 

Solenoid  is 

Energized 


Clock  for  making  Contact 
Predetermined  Intervals 


upply 


FIG.  312. — Printometer  and  record.     General  Electric  Co. 

the  dial  reading,  together  with  the  hour  when  the  record  was 
made.     The  instrument  is  shown  in  Fig.  312. 


526  ELECTRICAL  MEASUREMENTS 

The  essential  portions  are:  a  system  of  cyclometer  type  wheels 
actuated  by  a  solenoid  which  is  controlled  by  the  watt-hour  meter; 
an  arrangement  for  automatically  advancing  the  paper  tape  after 
each  record  (about  %  in.),  and  at  the  same  time  moving  along 
the  copying  ribbon  necessary  for  the  printing;  an  electrically 
operated  platen  for  taking  the  impression.  The  platen  is  con-, 
trolled  by  a  contact-making  clock  in  a  separate  case  and  is 
operated  every  half  hour. 

In  addition,  there  is  a  fourth  type  wheel,  in-line  with  the  other 
three,  which  prints  the  hours.  Every  half  hour  the  contact- 
making  clock  closes  the  circuit  and  causes  the  printing  platen 
to  be  drawn  up.  At  the  same  time  it  sets  in  motion  a  system  of 
levers  and  gears  by  which  the  hour  wheel  is  turned.  At  down 
stroke  of  the  armature  the  paper  tape  and  the  copying  ribbon  are 
advanced. 

To  actuate  the  printometer,  a  contact  device  is  placed  on  one 
of  the  shafts  of  the  register  of  the  watt-hour  meter  so  that  it 
closes  the  circuit  to  the  cyclometer  solenoid  after  the  appro- 
priate number  of  revolutions  of  the  meter  disc.  The  circuit  is 
so  arranged  that  it  is  made  by  the  contact  device  and  quickly 
broken  by  the  plunger  in  the  solenoid  at  the  end  of  its  stroke. 
The  arcing  is  thus  transferred  to  very  substantial  contacts  and 
friction  is  avoided.  The  current  is  kept  out  of  the  solenoid 
except  when  it  is  actually  operating. 

The  record  obtained  is  shown  in  Fig.  312.  By  subtracting  the 
successive  readings  the  demand  during  any  specified  half  hour 
may  be  obtained. 

Westinghouse  R.O.  Demand  Indicator. — This  instrument  is  a 
combined  watt-hour  and  watt-demand  meter  for  use  on  alter- 
nating-current circuits.  The  kilowatt-hours  are  registered  on 
four  dials,  as  usual,  while  the  demand  is  shown  by  a  long  pointer 
which  moves  over  a  fifth  dial  graduated  in  watts  or  kilowatts. 

The  mechanism  is  such  that  when  a  load  is  thrown  on,  the  watt- 
meter attains  the  corresponding  deflection  only  after  a  predeter- 
mined time,  for  example  15  min.,  the  rate  of  increase  of  the 
deflection  being  controlled  by  the  watt-hour  meter. 

Fig.  313  shows  in  a  diagrammatic  form  the  essential  features  of 
the  registering  mechanism.  The  main  disc  is  that  of  an  ordinary 
induction  watt-hour  meter.  By  means  of  the  worm  it  actuates 


ELECTRICITY  METERS 


527 


the  usual  four-dial  register,  from  which  the  kilowatt-hours  are 
read.  The  auxiliary  disc  is  a  metal  sector  which  forms  the  mov- 
able element  of  an  induction  wattmeter,  the  spiral  spring  furnish- 
ing the  control.  Both  discs  rnove  in  the  same  air  gap,  and  so  are 
actuated  by  the  same  set  of  current  and  potential  coils  (not  shown 
in  the  figure). 

The  auxiliary  disc  is  connected  by  means  of  the  spindle  and 
gears  1,  2,  3,  4,  with  the  dog  which  drives  the  demand  pointer. 
When  this  disc,  and  consequently  the  gear  4,  deflects  from  the  zero 


r- Spiral  Spring 


Trip 


Eatcbet 
Wheel 
ub  Loose 
on  Shaft 
6 


Pointer 


cnpement 
Wheel 


Main  Disk 

FIG.  313. — Diagram  for  Westinghouse  R.O.  demand  indicator. 

position  the  dog  pushes  the  pointer  up  the  scale.  If  the  aux- 
iliary disc  returns  toward  zero,  the  driving  arm  leaves  the  dog  and 
the  pointer  remains  stationary,  its  position  being  maintained  by 
the  ratchet  and  light  spring.  The  maximum  deflection  is  thus 
registered. 

The  time  element  is  introduced  as  follows:  Attached  to  the 
spindle  of  the  wattmeter  element  is  an  arm  carrying  the  main 
pawl.  This  pawl  rests  on  the  ratchet  wheel,  the  hub  of  which 
carries  the  gear  £  and  is  loose  on  the  spindle.  The  gear  5  meshes 
with  6,  and  is  thus  connected  to  the  escapement  wheel.  The 
escapement  is  oscillated  by  an  eccentric,  the  rate  of  oscillation 
being  controlled  from  the  worm  shaft  by  means  of  the  timing 
gears. 


528  ELECTRICAL  MEASUREMENTS 

The  teeth  of  the  escapement  wheel  are  radial,  so  there  is  no 
interchange  of  power  between  the  two  elements. 

When  a  load  is  thrown  on,  the  main  disc  begins  to  revoLve  and 
the  auxiliary  disc  tends  to  assume  its  ultimate  position  at  once 
However,  the  escapement  mechanism  prevents  this,  and  the 
deflection  increases  step  by  step  at  a  rate  dependent  on  the  rapid- 
ity of  oscillation  of  the  escapement;  that  is,  on  the  velocity  of  the 
main  disc.  If  the  load  is  doubled  the  escapement  oscillates  twice 
as  fast,  but  as  the  pointer  must  move  twice  as  far  the  ultimate 
deflection  is  attained  in  the  same  time.  By  changing  the  timing 
,  gears  the  maximum  deflection  may  be  reached  in  1,  2,  5,  15  or 
30  min.  as  desired.  When  the  load  decreases,  the  main  pawl 
drags  over  the  ratchet  wheel  and  the  driving  arm  moves  away 
from  the  dog,  leaving  the  pointer  at  its  maximum  deflection. 

By  raising  the  trip,  which  is  protected  by  a  separate  seal,  the 
pointer  may  be  set  back  to  zero  without  opening  the  meter. 

During  calibration  the  main  pawl  is  raised,  thus  disconnecting 
the  escapement.  The  instrument  is  then  calibrated  like  an  ordi- 
nary wattmeter  by  altering  the  length  of  the  spiral  spring  and  the 
zero  adjustment. 

The  instrument  is  reset  each  month  by  the  meter  reader  and 
leaves  no  record  of  its  former  indication,  and  there  is  no  way  of 
telling  the  hour  of  the  day  when  the  maximum  occurred. 


References 

1.  "Electricity  Meters,"  H.  G.  SOLOMON,  Charles  Griffin  &  Co.,  London, 
1906. 

2.  "Electricity  Meters,"  C.  H.  W.  GERHARDI,  Electrician  Printing  and 
Publishing  Co.,  London,  1906. 

3.  "Electrical  Meters,"   C.  M.  JANSKY,  McGraw-Hill  Book  Co.,   1913. 

4.  "Electrical  Measurements  and  Meter  Testing,"   D.   P.   MORETON, 
Frederick  J.  Drake  &  Co.,  Chicago,  1915. 

5.  "Electrical  Meterman's  Handbook,"  published  by  National  Electric 
Light  Association,    1915.     "Code  for  Electricity  Meters,"  Association  of 
Edison  111.  Co.,  Nat.  Elect.  Light  Assoc.,  second  edition,  1912. 

6.  "Die  Elektrizitatszahler,"  R.  ZIEGENBERG,  "Handbuch  der  Elektro- 
technik  II  Sechste  Abteiling,"  Leipzig,  1908,  S.  HUZEL. 

7.  "Electrical  Instruments  and   Meters  in  Europe,"   H.   B.  BROOKS, 
Department  of  Commerce  and  Labor,  Washington,  D.  C.,  1913. 

8.  "A    Comparative    Study    of    American    Direct-current    Watt-hour 


ELECTRICITY  METERS  529 

Meters,"  T.  T.  FITCH  and  C.  J.  HUBER,  Bulletin  of  the  Bureau  of  Standards, 
vol.  10,  1914,  p.  161. 

9.  "  Electricity  Meters  with  Special  Reference  to  Different  Kinds  of 
Loads,"  CLAYTON  H.  SHARP,  Report  of  International  Congress  of  Applied 
Electricity,  -Turin,  1911,  section  III,  vol.  II,  p.  777. 

10.  "Electrical  Meters  on  Variable  Loads,"  D.  ROBERTSON,  Journal  Insti- 
tution of  Electrical  Engineers,  vol.  49,   1912,   p.  489.     The  behaviour  of 
Direct-current  Watt-hour  Meters,  more  especially  in  relation  to  traction 
loads,  with  notes  on  erection  and   testing,   S.   W.   MELSON  and   W.   H. 
EASTLAND,  Journal  Institution  of  Electrical  Engineers,  vol.  49,  1912,  p.  465. 
Abstract,  The  Electrician,  vol.  69,  1912,  p.  216. 

11.  "Electricity  Meters,  with  Notes   on    Meter  Testing,"  H.  A.  RAT- 
CLTFF  and  A.  E.  MOORE,  Journal   Institution  of  Electrical  Engineers,  vol. 
47,  1911,  p.  3. 

12.  "A  Power  Company's  Testing  Department,"  E.  FAWSETT,  Journal 
Institution  of  Electrical  Engineers,  vol.  47,  1911,  p.  752. 

13.  Public  Document,  House  No.  1,672,  Massachusetts  Legislature,  1912. 
"Rates"' and   Rate-making,"    PAUL   M.   LINCOLN,  Transactions  American 
Institute  Electrical  Engineers,  vol.  34,  part  II,  1915,  p.  2279. 

14.  Report  of  Gas  and  Electric  Light  Commissioners,  State  of  Massa- 
chusetts, 1908. 

15.  "The  Testing  of  Large  Watt-hour  Meters  on  Fluctuating  Loads/' 
F.  A.  LAWS  and  C.  H.  INGALLS,  Electrical  World,  vol.  59,  1912,  p.  1309. 
See  also  "  Wheatstone  Bridge  Rotating  Standard  Method  of  Testing  Large- 
capacity  Watt-hour  Meters,"  C.  H.  INGALLS  and  J.  W.  COWLES,  Trans. 
A.  I.  E.  E.,  vol.  31,  1912,  part  II,  p.  1551. 


\ 

34 


CHAPTER  X 

PHASE  METERS,  POWER  FACTOR  INDICATORS,  SYN- 
CHROSCOPES AND  FREQUENCY  METERS 

In  the  mathematical  discussion  of  alternating  currents,  it  is 

usual  to  assume  sinusoidal  waves,  in  which  case, 

'  ' 

watts 
Power  factor  =  cos  0  =   — r— • 

volt-amperes 

where  6  is  the  time-phase  displacement  of  the  current  wave  with 
respect  to  the  e.m.f.  wave;  that  is,  the  angular  distance  between 
the  zero  points  of  the  waves.  With  non-sinusoidal  waves  the 
power  factor  is  taken  as  the  ratio  of  the  watts  to  the  volt- 
amperes.  In  this  case  6  is  without  significance. 

The  output  of  a  generator  is  limited  by  the  heating  due  to  the 
currents  in  its  coils,  and  the  financial  return  on  this  output  is 
primarily  based  on  the  true  watts.  For  this  reason  alone  then, 
it  is  highly  desirable  to  operate  the  system  supplied  by  the 
generator  at  as  high  a  power  factor  as  possible.  Also,  the  power 
factor  of  the  load  influences  the  voltage  regulation  of  the  system. 
It  is  not  unusual  to  employ  some  form  of  synchronous  apparatus 
as  a  transforming  device  between  the  generator  and  the  load. 
As  its  power  factor  may  be  controlled  by  varying  the  excitation, 
it  becomes  necessary  to  have  on  the  switchboard  a  power-factor 
meter,  or  its  equivalent,  as  an  aid  to  the  proper  handling  of  this 
apparatus. 

Idle  Current  Meters. — In  any  reactive  circuit  the  current  will 
either  lag  behind  or  lead  the  applied  e.m.f.  and  may  be  resolvec 
into  two  components,  one  the  power  component,  in  time  phase 
with  the  voltage,  the  other  the  quadrature  component  which  i 

WattleSS .  Power  Component 

_ .         E 


Quadrature  or 
^-^;  Idle  Component 

FIG.  314. — Showing  power  and  quadrature  components  of  current. 

Evidently,  for  sinusoidal  currents, 

Power  component  =  7  cos  6 
Quadrature  component  =  I  sin  0. 
530 


PHASE  METERS 


531 


The  component  I  sin  6  is  sometimes  called  the  idle  or  wattless 
current.  It  will  be  seen  that  operating  a  circuit  at  unity  power 
factor  is  equivalent  to  so  operating  it  that  the  idle  current  is 
zero. 

A  two-circuit  electrodynamometer,  with  the  movable  circuit 
placed  across  the  line  and  the  fixed  coils  traversed  by  the  line 
current,  will  give  a  deflection 

D  =  KIFIM  cos  0, 

where  6  is  the  phase  difference  of  IF  and  1M.  If  the  circuit  of 
the  movable  coil  is  non-inductive  the  instrument  is  an  ordinary 
wattmeter,  but  if  this  circuit  could  be  made  perfectly  reactive 
the  phase  of  IM  would  be  shifted  90°  with  respect  to  the  line 
voltage  and 

D  =  KIFIM  cos  (90°  -  6)  =  KIFIM  sin  0. 

At  a  constant  voltage  the  deflection  would  be  proportional  to  the 
idle  current,  I  sin  6,  or  at  any  voltage,  to  the  idle  volt-amperes. 


ab 


ab 


FIG.  315. — Connections  for  measuring  idle  volt-amperes  in  balanced  three- 
phase  circuit. 

On  account  of  the  energy  dissipated  in  the  reactor,  it  is 
impossible  to  shift  the  phase  of  the  potential-coil  current  by 
exactly  90°,  and  the  phase  shift  will  depend  on  the  frequency. 

Reference  to  the  theory  of  the  induction  wattmeter  will  show 
that  this  instrument  would  be  converted  into  an  idle  current 
meter  if  its  potential  circuit  were  made  perfectly  non-inductive. 

The  idle  volt-amperes  in  a  balanced  three-phase  circuit  may 
be  measured  by  the  use  of  wattmeters  if  the  coils  be  connected 
in  circuit  as  shown  in  Fig.  315. 


532 


ELECTRICAL  MEASUREMENTS 


From  the  vector  diagram  it  is  seen  that  each  wattmeter  gives 
a  deflection  proportional  to  El  cos  (90°  —  6)  =  El  sin  9.  If  the 
two  wattmeters  in  Fig.  315  are  the  two  elements  of  a  polyphase 
wattmeter,  the  reading  of  that  instrument  will  give  2EI  sin  6. 
As  the  total  idle  volt-amperes  in  the  load  is  -\/3EI  sin  6, 


Idle  volt-amperes  =  (reading) 


The  scale  of  the  instrument  may  be  graduated  so  that  the  idle 
volt-amperes  may  be  read  directly.  (Compare  with  two  watt- 
meter method  for  measuring  three-phase  power,  page  331). 

Tuma  Phase  Meter. — In  America,  power-factor  meters  are 
much  more  frequently  used  than  idle  current  meters.  Power- 
factor  meters,  as  well  as  various  forms  of  synchroscopes,  are 
developments  from  the  Tuma  Phase  Meter,  the  essential  portions 
of  which  are  shown  in  Fig.  316. 


90- 


Load 


r    t 

0 

i 

0 

V 

0 

1 

ex 

0 

I 

1 

o 

FIG.  316. — Diagram  of  Tuma  phase  meter. 

In  its  original  form  the  ideally  perfect  Tuma  phase  meter  is 
applicable  only  to  single-phase  circuits  and  gives  a  deflection  equal 
to  the  power-factor  angle  of  the  load.  By  a  trifling  alteration  it 
may  be  adapted  to  polyphase  circuits,  as  will  be  seen  later. 

The  fixed  coil  F  is  traversed  by  the  load  current.  The  coils 
A  and  B  are  of  equal  magnetic  strength  and  are  firmly  lashed 
together  to  form  a  single  movable  system  which  is  pivoted  in 
the  field  due  to  F;  in  the  ideal  instrument  A  and  B  are  inclined 
at  an  angle  of  90°  to  each  other. 


PHASE  METERS  533 

The  current  in  coil  A  is  supposed  to  be  controlled  by  a  pure 
resistance,  and  consequently  is  in  phase  with  the  applied  voltage 
V.  The  current  in  coil  B  is  supposed  to  be  controlled  by  a  pure 
inductance,  and  hence  is  in  quadrature  with  the  voltage  V. 

The  currents  are  taken  into  the  movable  system  at  the  pivot, 
through  flexible  connections  of  annealed  silver  foil  which  resemble 
ordinary  controlling  springs  in  appearance  but  which  exercise 
no  appreciable  torque  on  the  system. 

When  no  currents  are  flowing,  the  crossed  coils  are  perfectly 
neutral  and  will  remain  in  any  position  to  which  they  are  turned. 
The  position  of  the  crossed  coils  from  which  the  deflections  are 
reckoned  is  that  assumed  by  them  when  the  device  is  applied 
to  a  load  of  power  factor  unity.  In  that  case  the  planes  of  coils 
A  and  F  will  coincide,  for  as  the  currents  in  B  and  F  are  in 
quadrature,  on  account  of  the  inductance  L,  the  average  turning 
moment  on  B  is  zero. 

In  general,  on  the  passage  of  currents  through  the  coils  F,  A  and 
B,  a  field  will  be  set  up  by  F,  and  the  coils  A  and  B  which  form 
the  movable  element  will  both  experience  turning  moments. 
As  A  and  B  are  rigidly  connected,  the  movable  element  will  turn 
to  such  a  position  that  the  resultant  moment  acting  on  it  be- 
comes zero.  The  deflection,  D,  from  the  initial  position  occupied 
by  the  coils  when  the  power  factor  is  unity,  will  be  equal  to  the 
power-factor  angle  of  the  load. 

It  will  be  assumed  that  the  coil  F  is  so  large  compared  with 
A  and  B  that  the  crossed  coils  move  in  a  sensibly  uniform  field; 
also  that  the  circuits  of  A  and  B  are  inductionless  and  resist- 
anceless  respectively.  If  the  P.D.  wave  be  taken  as  the  datum 
for  measuring  phase  displacements,  the  turning  moment  acting 
on  coil  A  will  be,  at  any  instant, 

rV  "I 

KA[I  sin  (co£  --  0)]   p  sin  con   sin  D, 

where  KA  is  a  constant  depending  on  the  windings. 

The  turning  moment  on  coil  B  will  be,  at  any  instant, 

KB[I  sin  (co*  -  0)]|j^  sin   (co£  -  90°)]  sin   [D  +  90°]. 

The  currents  in  the  coils  are  such  that  A  and  B  tend  to  turn  in 
opposite  directions.     When  the  movable  system  has  come  to 


534  ELECTRICAL  MEASUREMENTS 

rest,  the  average  turning  moment  on  coil  A  must  equal  that  on 
coil  B,  so 

vK  IV~\  1  CT 

—  n  —     sin  D  ~  I      sin  (ut  —  6)  sin  (ut)dt  = 

r  K    TV~\  1    /" 

-^-Jcos  D  ^  I      sin  («J  -  0)  sin  (coZ  -  90°)  (ft 

-^—  J  sin  Z)  cos  0  =  [~~f"~-j  cos  £>  sin  0. 

If,  by  the  construction  of  the  apparatus 

KA       KB  ,  , 

-R     =  L^  («> 

then 

tan  D  =  tan  0 

and 


That  is,  the  movable  system  turns  through  an  angle  equal  to  the 
power-factor  angle  of  the  load. 

The  assumptions  made  in  order  to  obtain  this  result  are  that 
the  frequency  is  constant,  that  the  coils  A  and  B  are  small  com- 
pared with  F,  that  the  planes  of  coils  A  and  B  are  90°  apart  in 
space,  that  the  coils  are  traversed  by  currents  which  are  90° 
apart  in  time  phase  and  that  the  current  in  coil  A  is  in  phase 
with  the  line  voltage  V.  In  practice,  these  current  relations  can- 
not be  attained;  the  lag  in  the  circuit  B  can  never  be  exactly  90°. 
Nevertheless,  by  a  proper  adjustment  of  the  angle  between  the 
coils,  the  instrument  can  be  made  to  read  correctly. 

To  investigate  this  matter,  suppose  the  current  in  coil  B  lags 
A°  behind  V  and  that  the  mechanical  angle  between  the  coils  is 
0  instead  of  90°. 

Assuming  that  the  crossed  coils  are  alike  and  have  the  same 
number  of  ampere  turns, 

sin  D  cos  6  =  sin  (D  +  0)  cos  (0  -  A). 

The  fiducial  point  on  the  scale  corresponds  to  the  reading  when 
the  power  factor  of  the  load  is  unity;  in  that  case  the  deflection, 
Do,  will  be  given  by 


cot  DO  =  —  —  r  —  cot  ]3. 

sin      cos  A 


PHASE  METERS 


535 


When  the  power-factor  angle  of  the  load  is  0  the  reading  will 
be  given  by 

cot  D  ~~=  sin  ft  cos  A  +  tan  0  sin  0  sin  A  "  COt  /3< 
The  change  of  deflection  is  D  —  D0, 

cot  (D  -  Do)  =  cot  6 


1  —  cosj8  cos  A  +  [(cos2  A  — cos /9  cos  A")  +  (cos/3  cos  A  +  sin20 —  —  1)  (tan  8  cos/3  sin  A)l 


sin  /3  sin  A 


Inspection  shows  that  if  (3  ='  A,  this  equation  reduces  to 


or 


COt  (D  -  Do)    -   COt  B 


D  -  Do  = 


i  _ 


8 


sin2/3 


=   COt 


Consequently  if  the  crossed  coils  be  adjusted  once  for  all  so 
that  the  angle  between  their  planes  is  equal  to  the  electrical  angle 
between  their  currents,  the  deflection  from  the  initial  position 
will  be  equal  to  the  power-factor  angle  of  the  load. 

An  explanation  of  the  action  of  the  Tuma  phase  meter  may 
also  be  based  on  the  fact  that  the  crossed  coils  set  up  a  rotating 
field  (see  page  444),  for  in  the  original  design  of  the  instrument 
these  coils  are  90°  apart  in  space  and  are  traversed  by  currents 
differing  90°  in  time  phase. 

1.40 


.60 

Lagging  Power  Factor  Leading 

FIG.  317. — Showing  effect  of  frequency  on  a  single-phase  power-factor  meter. 

Single -phase  Power-factor  Meters. — In  the  application  of  the 
principle  of  the  Tuma  phase  meter  to  the  construction  of  power- 
factor  meters  for  use  on  single-phase  circuits  a  difficulty  is  en- 
countered. For  though  the  windings  and  the  angle  between 
the  crossed  coils  may  be  adjusted  so  that  the  instrument  reads 


536 


ELECTRICAL  MEASUREMENTS 


correctly  at  the  normal  frequency,  any  change  of  frequency  will 
render  the  readings  inaccurate,  because  both  the  phase  and 
the  magnitude  of  the  current  in  coil  B  are  controlled  by  an  in- 
ductance and,  therefore,  depend  on  the  frequency.  At  low  fre- 
quencies coil  B  carries  too  much  current,  at  high  frequencies  too 
little  current  and  condition  (a)  (page  534)  is  not  fulfilled.  The 
result  of  frequency  changes  on  a  single-phase  power-factor  meter 
is  illustrated  by  Fig.  317.  Single-phase  power-factor  meters  are 
made  but  are  not  in  common  use. 

Polyphase  Power-factor  Meters. — The  indications  of  poly- 
phase power-factor  meters  are  correct  only  on  balanced  circuits. 
If  the  circuit  is  unbalanced  the  reading  is  without  significance. 


FIG.  318. — Indicating  portion  of  Weston  power-factor  meter. 

The  application  of  the  Tuma  phase  meter  to  a  balanced  two-phase 
circuit  is  obvious.  The  two  crossed  coils  are  placed  90°  apart  in 
space;  their  currents,  90°  apart  in  time  phase,  are  obtained  by 
using  a  resistance  in  series  with  each  coil  and  energizing  a  coil 
from  each  of  the  two  phases.  To  adapt  the  instrument  to  bal- 
anced three-phase  circuits  it  is  to  be  remembered  that  the  angle 
between  the  planes  of  the  movable  coils  should  be  made  equal  to 
the  electrical  angle  between  the  currents  in  these  coils.  The  fixed 
coil  is  placed  in  one  of  the  line  wires,  while  the  movable  coils  are 
connected  from  this  wire  through  resistances  to  the  other  two 
wires  of  the  circuit,  see  Fig.  319. 


PHASE  METERS 


537 


•'§ 


Load 


FIG.  319. — Connections  for  three-phase  power-factor  meter. 


g    H  ,1   .98       I'll 


Mil'  I  i          i  IHMjJa 

i|iii  HJ!I""I  '-i  -I  i  n  i  IT 


Till 


FIG.  320. — Showing  parts  of  General  Electric  Co.  power-factor  meter  with 
magnetic  shielding. 


538 


ELECTRICAL  MEASUREMENTS 


Reckoning  from  lead  1  the  currents  in  A  and  B  are  60°  apart. 
The  fiducial  position  of  the  coils  is  given  when  the  power  factor 
of  the  load  is  unity;  if  the  power  factor  is  other  than  unity  the 
current  in  lead  1  is  shifted  6°,  where  6  is  the  power-factor  angle, 
and  the  crossed  coils  turn  through  an  equal  angle. 

The  polyphase  instruments  are  independent  of  frequency,  for 
no  reliance  is  placed  on  the  use  of  reactances  to  properly  shift  the 
phases  of  the  currents  in  the  crossed  coils.  On  high-voltage  cir- 
cuits the  meters  are  operated  through  instrument  transformers. 

In  power-factor  meters  as  actually  constructed,  see  Figs.  318 
and  320,  the  fixed  coils  are  made  to  surround  closely  the  movable 
system.  Economy  of  space  and  of  materials  are  thus  attained. 
In  this  case  the  scale  must  be  determined  by  calibration. 

To  avoid  the  use  of  movable  coils,  the  Westinghouse  Company 
in  certain  of  its  power-factor  meters  and  synchroscopes  uses  the 
construction  indicated  in  Fig.  321. 


FIG.  321. — Westinghouse  arrangement  of  coils  for  power-factor  meter. 

Within  the  stationary  crossed  coils  A  and  B  is  a  third  fixed 
coil  C  with  its  axis  perpendicular  to  the  plane  of  the  paper.  This 
coil  carries  the  line  current  and  magnetizes  the  soft  iron  element 
D,  which  is  mounted  in  jeweled  bearings.  The  iron,  Z),  thus  forms 
the  core  of  an  alternating-current  electromagnet  and  acts  as  if 
it  were  a  pivoted  coil  carrying  the  line  current. 

Another  arrangement  of  circuits,  as  used  in  the  Punga  power- 
factor  meter,  is  shown  in  Fig.  322. 

The  movable  system  consists  of  three  flat,  rectangular  coils 
lashed  to  the  spindle  so  that  they  are  120°  apart;  they  have  a 
common  electrical  terminal  at  0,  that  is,  they  are  Y  connected 
across  the  line;  the  currents  are  controlled  by  resistances. 


PHASE  METERS 


539 


At  unity  power  factor  the  current  in  the  fixed  coil  is  in  time 
phase  with  the  voltage  Vao  or  the  current  Iao,  so  taking  Vao 
as  the  datum  for  phase  displacement, 


FIG.  322.  —  Connections  for  Punga  power-factor  meter. 

Field  due  to  fixed  coil  =  KI  sin  (ut  -  8) 
Current  in  coil  ao  =  I'  sin  ut 

Current  in  coil  bo  =  I'  sin  (cot  —  120°) 

Current  in  coil  co  =  I'  sin  (cot  —  240°). 

For  equilibrium  the  net  turning  moment  due  to  the  three  coils 
must  be  zero,  and 

i  r 

sin  D  jf,  I     sin  (cot  —  6)  sin  utdt 
1Jo 

+  sin  (D  -  120°)  ~  ("sin  (ut  -  6)  sin  («*  -  120°)  dt 
1Jo 


1  fT 
^       si 
1  Jo 


+  sin  (D  -  240°)  ^       sin  (««  -  0)  sin  («*  -  240°)  (ft  =  0. 
1  Jo 

Integrating  and  substituting  the  values  of  the  functions  of 
120°  and  240°, 

%  cos  6  sin  D  —  %  cos  D  sin  0  =  0 

.-.  D-e, 

the  same  result  as  was  obtained  with  the  two  crossed  coils. 

Power-factor  Charts. — In  tests  of  industrial  plants,  it  is  fre- 
quently important  to  gain  an  idea  of  the  power  factor  under 
ordinary  operating  conditions.  In  three-phase  work  the  two 
wattmeter  method  of  measuring  power  will  usually  be  employed. 
For  a  balanced  load  the  power  indicated  by  the  two  wattmeters  is 

Pi  =  El  cos  (6  +  30°) 
P2  =  El  cos  (0  -  30°). 


540 


ELECTRICAL  MEASUREMENTS 


It  is  convenient  to  calculate  and  plot  once  for  all  a  curve  such 
as  is  shown  in  Fig.  323. 

The  ordinates  of  the  curve  are  power  factors  or  values  of  cos  6 ; 
the  abscissa  are  values  of  the  ratio 

Smaller  reading  _  cos  (6  +  30°)  _ 
Larger  reading  ~  cos  (0  —  30°)  ~~    ' 
The  relation  between  the  power  factor  ano  the  ratio  R  is 

1 


Power  factor  = 


1.0' 

.9 
.8 

I  .6 
I   .5 


-2 


-1.0-9  -.8  -7  -.6  -.5  -.4  -.3  -.2  -.1  ±0  -hi  +.2  -+-.3  +.4  +.5  +.G  +.7  +.8  +.9+1.0 
Ratio  =  Smaner  Reading   =    Cog  (  0  -+  30°) 
Larger  Reading          Cos    (  Q  —  30°) 

FIG.  323. — Power-factor    chart,    two-wattmeter  method,  balanced    three- 
phase  load. 

Synchroscopes,  Synchronizers. — When  alternators  are  operated 
in  parallel,  it  is  necessary  in  putting  a  machine  on  the  system 
that  the  voltage  of  the  incoming  machine  be  equal  in  magnitude 
and  opposite  in  phase  to  the  voltage  of  the  busses.  To  avoid 
accidents  and  injurious  stresses  in  the  machines,  it  is  necessary  to 
have  some  instrument  which  will  show  when  the  proper  phase 
relation  has  been  attained  and  in  the  case  of  large  machines, 
whether  the  speed  of  the  incoming  machine  must  be  increased 
or  diminished  before  the  main  switches  are  closed. 

The  Lincoln  Synchroscope. — The  Lincoln  and  kindred  forms 
of  ^synchroscopes  furnish  the  switchboard  attendant  with  the 
desired  information.  This  instrument  is  in  principle  a  Tuma 
phase  meter  with  the  slight  modification  that  the  currents  are 
carried  to  the  crossed  coils  by  brushes  and  slip  rings  so  that  the 

- 


PHASE  METERS 


541 


movable  element  can  rotate  continuously.     The  essential  elec- 
trical connections  are  indicated  in  Fig.  324. 


nnnnnr 
pnnwn 

To  Incoming  Machine    To  Bus-bars 
FIG.  324. — Diagram  for  Lincoln  synchroscope. 


FIG.  325. — General  Electric  Co.  synchroscope. 

In  the  actual  instrument,  Fig.  325,  the  shaft  carrying  the  slip 
rings  and  the  movable  element  is  mounted  in  ball  bearings  and 


542 


ELECTRICAL  MEASUREMENTS 


as  shown  is  perpendicular  to  the  plane  of  the  paper.  To  increase 
the  turning  moment  acting  on  the  movable  system  and  thus 
reduce  the  effect  of  the  brush  friction,  both  the  field  and  movable 
coils  are  wound  on  laminated  iron  cores.  The  similarity  of  the 
arrangement  to  the  Tuma  phase  meter  is  at  once  apparent. 

The  index  tries  to  point  to  the  angle  of  phase  difference  between 
the  machines,  and  its  rate  of  movement  is  dependent  on  the 
difference  of  the  machine  speeds.  It  will  move  forward  or  back- 
ward or  come  to  rest  depending  on  whether  the  incoming  machine 
is  running  faster,  slower  or  at  the  same  speed  as  the  other  machine. 
The  pointer  may  come  to  rest  in  any  position  on  the  dial.  This 
merely  means  that  both  machines  are  running  at  the  same  speed, 
though  not  necessarily  in  phase.  The  speed  of  the  incoming 
machine  must  be  altered  very  gradually  and  the  main  switch 
closed  as  the  pointer  slowly  drifts  across  the  index  mark. 


FIG.  326. — Weston  synchroscope. 

Weston  Synchroscope. — This  instrument  is  an  electrodyna- 
mometer  with  a  spring  control.  The  fixed  coils  are  connected 
across  the  station  bus-bars,  in  series  with  a  suitable  resistor,  while 
the  movable  coil,  in  series  with  a  condenser,  is  placed  across  the 
incoming  machine. 

If  the  machines  are  in  synchronism  or  180°  out  of  synchronism, 
the  currents  in  the  two  coils  will  be  in  quadrature  and  the  index 


PHASE  METERS 


543 


will  stand  at  the  reference  mark.  If  they  are  running  at  the  same 
frequency,  but  are  not  in  the  proper  phase  relation,  the  pointer 
will  come  to  rest  at  a  position  depending  on  the  phase  differ- 
ence of  the  machines.  If  the  frequencies  are  nearly,  but  not 
exactly  the  same,  the  pointer  will  "beat,"  or  move  back  and 
forth  over  the  scale.  This  arrangement  is  supplemented  by  a 
synchronizing  lamp,  as  indicated.  The  lamp  is  behind  the  pointer 
and  the  transparent  scale  and  is  arranged  to  be  bright  when  the 
machines  are  in  synchronism.  The  incoming  machine  is  to  be 
connected  to  the  bus-bars  when  the  dark  pointer  coincides  with 
the  reference  mark  and  both  appear  on  the  light  field  due  to  the 
glowing  of  the  synchronizing  lamp. 

Hartmann  and  Braun  Synchroscope. — The  firm  of  Hartmann 
and  Braun  has  devised  a  synchroscope  based  on  the  vibrating 
reed  frequency  meter,  page  548.  This  instrument,  with  a  dia- 
gram of  its  circuits,  is  shown  in  Fig.  327. 


FIG.  327. — Hartmann  and  Braun  synchroscope. 

The  frequency  at  the  bus-bars  and  that  of  the  incoming  ma- 
chine are  shown  on  the  two  vertical  banks  of  reeds.  On  closing 
the  switch,  the  upper  set  of  reeds  is  put  in  series  with  the  two 
machines  and  will  be  acted  upon  by  the  net  voltage  around  the 
machine  circuit.  The  synchroscope  circuits  are  so  arranged  that 
when  both  machines  are  running  at  the  normal  frequency,  shown 
on  banks  I  and  II,  and  are  in  the  proper  phase  relation,  the 
reed  in  the  upper  set  which  corresponds  to  the  normal  frequency 
will  vibrate  continuously  with  its  maximum  amplitude. 

Phasing  Lamps. — Before  the  B  invention  of  such  synchron- 
izing devices  as  have  been  described,  it  was  customary  to 


544  ELECTRICAL  MEASUREMENTS 

depend  upon  synchronizing  lamps.  With  small  low-voltage 
machines  it  is  sufficient  to  place  an  incandescent  lamp  across  the 
gap  of  the  single  pole  switch  by  which  the  incoming  machine  is 
to  be  connected  to  the  bus-bars.  If,  when  the  voltage  has  been 
adjusted,  the  incoming  machine  is  not  running  at  the  proper 
frequency,  the  lamp  will  be  alternately  light  and  dark.  As  the 
frequency  of  the  incoming  machine  is  brought  toward  its  proper 
value,  the  flicker  of  the  lamp  becomes  slower  and  slower.  The 
proper  time  for  closing  the  switch  is  when  the  lamp  re- 
mains dark,  for  then  the  voltages  on  the  machine  circuits  are  in 
opposition. 


To  Bus  Bars 


Lamp 


To  Incoming  Machine 


FIG.  328. — Arrangement  of  phasing  lamp  actuated  by  two  transformers. 

When  high  voltage  machines  are  used,  it  becomes  necessary 
to  employ  transformers.  They  may  be  connected  so  that  $he 
proper  time  for  closing  the  main  switch  is  shown  either  when  the 
lamp  is  dark  or  when  it  is  at  full  brilliancy.  The  latter  is  the 
better  practice  as  it  avoids  mistakes  due  to  the  failure  of  the  lamp. 
The  two  transformers  may  be  combined  into  one  with  two  pri- 
maries wound  on  two  different  branches  of  the  magnetic  circuit 
and  a  single  secondary  wound  on  a  third  branch  as  shown  in 
Fig.  326. 

A  fault  of  these  arrangements  of  phasing  lamps  is  that  they 
give  no  indication  as  to  whether  the  speed  of  the  incoming 
machine  should  be  increased  or  diminished. 

Siemens  and  Halske  Arrangement  of  Phasing  Lamps. — The 
operation  of  the  arrangement  will  be  understood  from  the  sim- 
plified diagram,  Fig.  329,  where  only  three  lamps  are  shown,  and 
the  transformers  necessary  on  a  high  voltage  system  are  omitted. 

The  dotted  connection  simply  denotes  that  the  two  neutral 
points  are  at  the  same  potential.  The  noticeable  feature  of  the 


Incoming 
Machine 

a 


PHASE  METERS 

a 


545 


Running 
Machine 

af 


lie.  329. — Diagram  for  Siemens  and  Halske  arrangement  of  phasing  lamps. 

•E0'a' 


The  e.m.f.  acting  on  lamp  No.  1  will  be: 

E  Qd   •+  E  d  'Q  '  =  O 


The  e.m.f.  acting  on  lamp  No.  2  will  be: 


The  e.m.f.  acting  on  lamp  No.  3  will  be: 


EOO 
FIG.  330, — Vector  diagrams,  Siemens  and  Halske  phasing  lamps. 


546  ELECTRICAL  MEASUREMENTS 

arrangement  is  that  phase  oc  is  connected  to  o'b'  and  phase  06 
to  oV. 

Suppose  the  two  machines  are  in  synchronism.  The  vector 
diagrams  for  the  electromotive  forces  are  shown  in  Fig.  330. 

Synchronism  is  indicated  when  lamp  No.  1  is  dark  and  lamps 
2  and  3  are  glowing.  If  the  machines  are  not  in  phase,  the  vec- 
tors being  in  the  dotted  position,  lamp  No.  1  begins  to  glow,  No. 
2  grows  dimmer  and  No.  3  grows  brighter,  so  the  dark  lamp  is 
passed  from  position  No.  1  to  position  No.  2.  If  the  phase  dis- 
placement is  in  the  other  direction,  lamp  No.  1  begins  to  glow, 
No.  2  grows  brighter  and  No.  3  is  dimmed,  so  that  the  dark  lamp 
is  passed  from  position  No.  1  to  position  No.  3. 

The  lamps  are  arranged  on  the  switchboard  at  the  corners  of 
an  equilateral  triangle;  by  noticing  whether  the  order  of  brilliancy 
of  the  lamps  proceeds  around  the  triangle  in  the  right-hand  or 
the  left-hand  direction,  one  can  tell  whether  the  speed  of  the  in- 
coming machine  must  be  increased  or  diminished. 

Frequency  Meters. — Instruments  of  this  class  should  be  inde- 
pendent of  wave  form  and  also  of  variations  of  the  line  voltage. 
Because  of  the  latter  requisite,  certain  forms  of  frequency  meter 
are  constructed  so  that  the  controlling  and  deflecting  moments 
acting  on  the  movable  system  both  depend  on  the  current  through 
the  instrument,  that  is,  on  the  line  voltage. 

Resonating  Frequency  Meters. — Under  the  usual  operating 
conditions  the  range  of  frequencies  which  must  be  covered  by 
any  form  of  frequency  meter  is  small,  and  the  normal  frequency 
of  the  current  has  a  definite  fixed  value.  It  thus  becomes  natural 
to  employ  in  these  instruments  the  principle  of  resonance, 
either  electrical  or  mechanical. 

In  the  General  Electric  Company's  resonating  frequency  meter, 
advantage  is  taken  of  the  action  of  circuits  containing  inductance 
and  capacity  in  series.  When  such  a  circuit  is  properly  adjusted, 
if  the  periodicity  of  the  applied  P.D.  be  varied,  the  maximum 
value  of  the  current  will  be  sharply  defined,  provided  the  energy 
losses  in  the  circuit  be  small.  Fig.  331  shows  the  circuits  of 
this  particular  instrument.  The  movable  element  consists  of 
two  crossed  coils  set  very  nearly  at  right  angles  to  each  other;  it 
is  pivoted  and  free  to  move,  there  being  no  controlling  springs. 

For  a  60-cycle  instrument  one  main  circuit  is  tuned  to  reso- 


PHASE  METERS  547 

nate  at  68  cycles,  the  other  at  52  cycles;  each  circuit  is  connected 
to  one  of  the  crossed  coils  which  tend  to  turn  the  system  in  oppo- 
site directions.  The  fixed  coil  carries  the  total  current. 

If  the  frequency  is  high,  in  the  neighborhood  of  68  cycles, 
the  68-cycle  member  of  the  system  will  carry  a  large  current 
while  the  current  in  the  52-cycle  coil  will  be  small.  The  effect 
of  the  68-cycle  coil  will  preponderate  and  it  will  turn  toward  the 
left,  carrying  the  52-cycle  coil  with  it.  As  it  turns,  the  68-cycle 
coil  moves  to  a  less  advantageous  position  while  the  52-cycle 
coil  is  moved  toward  the  position  where  its  effect  will  be  a  maxi- 
mum. The  movable  element  thus  arrives  at  an  equilibrium 


C  R 

r» 

52 -^v- 


68  **• 
FIG.  331. — Diagram  for  General  Electric  resonating  frequency  meter. 

position  which  depends  on  the  frequency.  A  high  degree  of 
sensitiveness  may  be  attained,  so  that  the  full  scale  of  a  60-cycle 
instrument  extends  from  55  to  65  cycles.  At  abnormally  low 
frequencies,  the  currents  in  both  coils  would  be  very  small  and 
the  pointer  might  drift  back  on  the  scale  and  thus  give  rise 
to  errors;  for  this  reason  a  circuit  tuned  to  38  cycles  is  added,  its 
effect  being  to  keep  the  index  off  the  scale  at  low  frequencies. 

The  inductances  are  wound  on  laminated  iron  cores  provided 
with  air  gaps;  the  gaps  are  necessary,  for  in  order  that  the  tuning 
may  be  accomplished  the  power  factors  must  be  low  and  wave 
distortion  must  be  avoided.  The  iron  must  be  worked  at  a  low 
flux  density  and  the  hysteresis  reduced  to  a  minimum.  These 
instruments  are  made  both  in  the  indicating  and  in  the  curve 
drawing  forms. 

In  1888  Ayrtoji  suggested  that  it  was  possible  to  determine  the 
frequency  of  an  alternating  current  by  employing  the  principle 
of  mechanical  resonance,  and  of  late  years  this  suggestion  has 
been  developed  into  commercial  forms  of  frequency  meters.  In 


548  ELECTRICAL  MEASUREMENTS 

these  modern  instruments  there  is  a  bank  of  steel  reeds  so  tuned 
that  the  natural  periods  of  successive  reeds  differ  by  one  alterna- 
tion. This  bank  of  reeds  is  acted  upon  by  an  electromagnet 
traversed  by  current  taken  from  the  line.  Only  the  reeds  very 
nearly  in  tune  with  the  frequency  of  the  circuit  respond  visibly, 
the  reed  most  nearly  in  tune  showing  the  maximum  amplitude. 
If  it  is  exactly  in  tune,  the  amplitude  is  very  large.  This  is  well 
illustrated  by  Fig.  332,  which  shows  the  amplitude  of  vibration 
of  a  reed  tuned  to  a  frequency  of  90  alternations  when  currents 


Frequency 


90     89.5     89     88.5     88      87.5     87 

FIG.  332. — Showing  effect  of  frequency  on  the  amplitude  of  vibration  of  a 
reed  in  a  frequency  meter. 

of  various  frequencies  are  sent  through  the  magnet.  A  varia- 
tion from  90  to  89.5  alternations  reduces  the  amplitude  over  50 
per  cent,  (compare  with  the  vibration  galvanometer,  page  434). 

In  order  to  insure  reliability  and  long  life  the  butts  of  the  reeds 
must  be  firmly  held.  The  arrangement  adopted  by  the  firm  of 
Hartmann  and  Braun  and  one  form  of  the  complete  instrument 
are  shown  in  Fig.  333. 

If  the  reeds  are  unpolarized  they  will  be  drawn  toward  the 
magnet  at  each  alternation,  so  that  the  reed  having  twice  the 
frequency  of  the  current  responds.  If  they  are  polarized,  by 
either  permanent  or  electro-magnets,  the  reed  having  the  same 
frequency  as  the  circuit  will  have  the  maximum  amplitude  of 
vibration. 

The  reeds  are  approximately  tuned  by  making  them  of  dif- 
ferent lengths,  the  final  tuning  being  effected  by  altering  their 
weights  by  filing  away  drops  of  solder  which  are  at  their  outer 


PHASE  METERS 


549 


ends  just  behind  the  white  indexes.  In  the  instrument  of  this 
class  made  by  Siemens  and  Halske,  all  the  reeds  are  fixed  to  a 
single  metallic  bar  which  is  so  mounted  on  a  spring  support  that 
it  may  be  gently  vibrated  by  the  action  of  an  electromagnet 
excited  from  the  circuit.  The  particular  reed  which  is  in  tune 
with  the  circuit  responds  with  the  maximum  amplitude. 


140 


FIG.  333. — Hartmann  and  Braun  frequency  meter. 

These  frequency  meters  may  be  used  as  speed  indicators. 
In  this  case,  a  toothed  wheel  or  some  other  form  of  rotary  key 
is  attached  to  the  shaft  of  the  machine  and  serves  to  interrupt 
a  direct  current  which  is  sent  through  the  meter.  Knowing  the 
number  of  contacts  per  revolution  of  the  shaft  and  the  number  of 
impulses  as  read  from  the  scale,  the  revolutions  may  be  calcu- 
lated. 

The  Siemens  and  Halske  arrangement  in  a  modified  form  is  used 
as  a  revolution  indicator  for  steam  engines  and  other  machinery. 


550 


ELECTRICAL  MEASUREMENTS 


In  this  case,  the  bank  of  reeds  is  supported  from  the  base  of  the 
machine  in  question.  Owing  to  the  lack  of  exact  balance  in  the 
moving  parts  of  the  machine,  a  vibration  exists  which  is  sufficient 
to  set  the  reeds  in  motion  and  thus  indicate  the  speed. 

Induction  Frequency  Meter. — The  essential  features  of  the 
induction  frequency  meter  made  by  the  Westinghouse  Company 
are  shown  in  Fig.  334. 

At  A  and  C  are  two  shaded-pole  motor  elements  which  tend  to 
rotate  the  movable  element  B  in  opposite  directions.  A  is  in 


FIG.  334. — Westinghouse  induction  frequency  meter. 

series  with  an  inductance,  C  in  series  with  a  resistance.  The 
movable  element  is  a  flat  plate  of  aluminum;  its  boundary  above 
the  dotted  diametral  line  is  a  semicircle  with  its  center  in  the 
axis  of  rotation,  while  below  the  same  line  it  is  practically  a 
semicircle  with  its  center  shifted  a  little  upward  along  the  line. 
The  torque  exerted  by  each  element  is  proportional  to  the  fre- 
quency and  to  the  square  of  the  current.  If  the  voltage  of  the 
circuit  varies,  both  elements  are  affected  and  the  movable  sys- 
tem is  not  disturbed,  but  if  the  frequency  rises,  less  current  will 
flow  through  the  inductance  and  the  effect  of  the  other  element 
will  preponderate.  The  disc  will,  begin  to  turn  toward  the  left 
but  on  account  of  the  shape  of  the  disc  this  brings  less  of  it  under 
the  influence  of  the  element  C,  so  that  it  takes  up  a  new  equilib- 


PHASE  METERS  551 

rium  position.  There  is  no  moving  wire  and  consequently  no 
necessity  for  taking  current  to  and  from  the  movable  element. 

Magnetic  Vane  Frequency  Meter.- — The  arrangement  adopted 
in  the  Weston  frequency  meter  is  shown  in  Fig.  335. 

The  crossed  coils  A  and  B  are  fixed  and  in  their  field  is  pivoted 
a  long  thin  needle  of  soft  iron,  N,  which  carries  the  pointer. 
There  is  no  controlling  spring.  The  inductances  (L)  and  resist- 
ances (R)  are  so  proportioned  that  the  combined  action  of  the  two 

N 


L 

FIG.  335. — Diagram  for  Weston  magnetic  vane  frequency  meter. 

coils  sets  up  an  elliptical  rotating  field.  The  needle  takes  up  the 
direction  of  the  longer  axis  of  the  field,  the  angular  position  of 
which  changes  as  the  frequency  alters.  If  the  frequency  risss, 
for  the  same  total  current  in  the  circuit  the  current  in  coil  A  is 
increased  while  that  in  coil  B  is  diminished.  This  shifts  the  direc- 
tion of  the  axis  of  the  field  and  the  pointer  is  thus  carried  over  the 
scale. 

References 

1.  "  Ein  Phasenmessapparat  fur  Wechselstrome,"  J.  TUMA,  Sitzungbericht 
der  K.  Akad.  Wissenschaft,  Vienna,  vol.  106,  1897,  p.  521. 

2.  "Power  Factor  Indicator,"  AUG.  J.  BOWIE,  JR.,  Electrical  World,  vol. 
36,  1900,  p.  644. 

3.  "Power  Factor  Indicators,"   WILLIAM  HAND   BROWNE,   JR.,    Trans. 
A.I.E.E.,  vol.  17,  1901,  p.  287. 

4.  "Phase  Meters  and  Their  Calibration,"  W.  E.  SUMPNER,  Electrician, 
vol.  56,  1906,  p.  760. 

5.  "Theory  of  Phase  Meters,"  W.  E.  SUMPNER,  Philosophical  Magazine, 
vol.  11,  1906,  p.  81. 

6.  "Synchronism  and  Frequency  Indication,"  PAUL  M.  LINCOLN,  Trans. 
A.I.E.E.,  vol.  18,  1901,  p.  255. 

7.  "Resonant  Circuit  Frequency  Indicator,"  W.  H.  PRATT  and  D.  R. 
PRICE.     Trans.  A.I.E.E.,  vol.  31,  1912,  Part  II,  p.  1595. 


CHAPTER  XI 

GRAPHIC  RECORDING  OR  CURVE-DRAWING 
INSTRUMENTS 

Graphic  recording  instruments  are  those  which  automatically 
record  their  indications  on  a  uniformly  moving  strip,  or  circular 
sheet,  of  paper.  Continuous  and  permanent  records  of  the  quan- 
tity which  the  instruments  are  adapted  to  measure  are  thus 
obtained. 

Such  instruments  are  extremely  useful  in  investigating  the 
power  conditions  in  factories  and  in  studying  the  cycle  of  opera- 
tions of  single  machines.  In  many  cases  the  load  fluctuates  so 
rapidly  that  to  obtain  equivalent  data  by  using  indicating  in- 
struments would  necessitate  the  observers  remaining  continu- 
ously at  their  posts  taking  frequent  readings  at  noted  times. 
Afterward,  these  readings  must  be  plotted  and  the  best  repre- 
sentative curve  drawn.  This  is  a  time-consuming  operation. 

Continuous  records  are  frequently  important  in  central- 
station  work.  For  instance,  a  registering  ammeter  in  a  feeder 
gives  a  record  of  the  current  and  shows,  if  the  clock  be  of  good 
quality  and  properly  regulated,  when  the  feeder  is  put  in  and 
taken  out  of  service,  as  well  as  the  time  when  any  abnormal 
conditions  arise.  Such  data,  if  systematically  kept,  may  be  of 
great  importance  as  evidence  in  adjusting  disputes  arising  from 
accidents.  Again,  a  continuous  record  of  the  potential  on  a 
lighting  circuit  contributes  to  the  life  of  the  incandescent  lamps 
by  directing  the  attention  of  the  operator  toward  constancy  of 
voltage.  The  records  obtained  by  a  registering  wattmeter  show 
the  customer's  power  consumption  throughout  the  day  and  are 
useful  in  determining  rates. 

Fig.  337  illustrates  the  application  of  an  instrument  of  this 
class  to  the  study  of  a  particular  machine.  It  shows  the  current 
taken  by  a  direct-current  motor  driving  a  roughing  lathe.  The 
cycle  of  operations  is  to  be  referred  to  Fig.  336  which  shows 

552 


GRAPHIC  RECORDING  INSTRUMENTS 


553 


the  piece  which  is  being  turned.  Corresponding  points  in  the 
two  figures  bear  the  same  letter. 

The  variation  of  power  with  depth  of  cut  and  the  time  required 
for  each  operation  are  clearly  shown. 

A  simple  form  of  recording  ammeter  which  has  been  in  use 
for  many  years  is  shown  in  Fig.  338.  The  current  flows  through 
the  coil  A  giving  rise  to  an  attraction  on  the  soft  iron  disc  B 


FIG.  336. — Piece  to  which  cycle  shown  in  Fig.  337  applies. 


30 


£20 

a 


10 


D  E 


To  Complete  Shaft> 


10:00  A.M.  9:45  A.M.  9:30  A.M.  9:15  A.M. 

FIG.  337. — Curve  showing  typical  cycle  on  a  roughing  lathe. 

carried  by  the  rod  CD  which  passes  freely  along  the  axis  of  the 
coil.  The  rod  is  supported  on  knife  edges  by  two  flat  springs 
CC  and  DD  which  are  fixed  at  their  lower  ends;  DD  carries  the 
pointer  E  to  which  the  pen  is  attached.  The  record  is  made  on 
a  circular  sheet  of  paper  which  is  rotated  at  a  uniform  rate  by 
the  clockwork.  Ordinarily  for  central  station  work  the  records 
are  for  a  24-hour  period.  For  special  work  this  may  be  varied 
by  using  the  appropriate  clockwork.  The  pen,  which  rests  on 
the  paper  continuously,  is  a  little  V-shaped  trough  cut  away  at 
one  end  so  that  only  a  fine,  point  at  the  apex  of  the  V  drags  on 


554 


ELECTRICAL  MEASUREMENTS 


the  paper.  The  trough  holds  a  few  drops  of  an  aniline-glycerine 
ink  which  is  carried  to  the  paper  by  capillary  action.  As  the 
reservoir  holds  but  little  ink,  frequent  attention  by  the  operator 
is  necessary. 

Another  instrument  of  the  same  class  is  shown  in  Fig.  339A. 
A  counterbalanced  soft  iron  core,  consisting  of  a  tube  which  pro- 
jects perpendicularly  from  a  disc  of  the  same  material,  is  at- 
tracted into  the  coil  against  the  action  of  a  spiral  spring.  By  a 


FIG.  338. — Bristol  curve-drawing  ammeter. 

simple  lever  the  motion  of  the  core  causes  the  pen  to  travel  over 
the  chart.  The  tube  and  disc  are  slit  to  reduce  eddy  currents. 
An  adjustable  iron  plug  in  the  lower  part  of  the  solenoid  allows 
the  deflection  at  the  upper  end  of  the  scale  to  be  adjusted.  The 
needle  is  damped  by  an  aluminum  damping  disc  of  the  usual 
form  actuated  by  gearing  from  the  pivot  carrying  the  index. 
The  clock  is  ordinarily  arranged  so  that  the  chart  is  for  either  a 
12-  or  a  24-hour  period. 


GRAPHIC  RECORDING  INSTRUMENTS 


555 


Instruments  like  those  just  described  are  useful  when  a 
moderate  accuracy  will  suffice;  for  instance,  on  a  set  of  feeder 
panels  where  many  instruments  must  be  installed  and  consider- 


FIG.  339. — Curve  drawing  ammeters,  General  Electric  Co. 

able  expense  is  not  justified.     If  a  high  degree  of  accuracy  is 
desired,  more  complicated  arrangements  must  be  used. 

A  registering  instrument  should  be  capable  of  operating  for  a 
considerable   period   without   attention,   for    1    or   2   weeks   in 


556  ELECTRICAL  MEASUREMENTS 

many  cases.  The  clock  should  be  of  good  quality,  preferably 
self-winding,  the  motion  of  the  paper  positive,  and  the  time  scale 
uniform. 

The  special  difficulties  in  the  design  of  accurate  instruments 
of  this  sort  come  from  the  pen  friction  which  impedes  the 
motion  of  the  pointer.  It  is  best  that  the  scale  be  uniform  and 
the  records  given  on  rectangular  coordinates  so  that  they  may 
readily  be  integrated  by  a  planimeter.  A  uniform  time  coordi- 
nate may  be  attained  by  driving  the  paper  by  a  metal  drum 
having  projecting  pins  which  engage  in  perforations  at  the  edges 
of  the  record  paper. 

In  the  better  class  of  instruments  the  effect  of  pen  friction  is 
minimized  or  eliminated : 

1.  By  giving  the  movable  system  a  high  torque  and  employing 
a  very  strong  controlling  spring.     By  using  soft-iron  instruments 
of  proper  design,  ammeters  and  voltmeters  may  thus  be  con- 
structed in  which  the  pen-friction  error  is  reduced  to  1  or  2  per 
cent  of  the  full-scale  deflection,  without  an  unduty  great  con- 
sumption of  power.     (50  watts  in  a  voltmeter;  7  watts  in  an 
ammeter.) 

2.  By  providing  the  pointer  with  a  stile  that  ordinarily  swings 
clear  of  the  paper  but  which  is  periodically  pressed  against  it 
by  an  electromagnet  and  imprints  a  dot.     This  arrangement  is 
useful  where  the  phenomena  under  investigation  vary  slowly. 
It  has  proved  of  great  service  in  those  forms  of  registering  thermo- 
electric pyrometers  which  are  in  reality  registering  millivolt- 
meters.     A  modification  is  to  have  an  arrangement  by  which  a 
high-tension  spark  is  periodically  caused  to  pass  from  the  stile 
through  the  paper,  thus  again  giving1  the  record  in  the  form  of 
dots. 

3.  By  using  the  relay  principle;  in  this  case  the  movable  system 
has  only  to  control  the  position  of  the  pen,  the  power  necessary 
to  move  it  being  supplied  from  an  external  source.     Relay  instru- 
ments are  somewhat  complicated,  but  the  wattmeters  and  the 
direct-current  ammeters  as  usually  designed  have  a  uniform 
scale  and  thus  give  records  on  rectangular  coordinates. 

A  direct-action  registering  wattmeter  for  polyphase  circuits 
is  shown  in  Fig.  340.  Here  the  friction  is  overcome  by  the  high 
torque  of  the  movable  systems. 


GRAPHIC  RECORDING  INSTRUMENTS 


557 


The  large  vertical  cylinder  at  the  left  is  a  laminated  soft  iron 
shield.  The  working  parts  consist  of  two  substantial  dynamo- 
meter wattmeters,  both  movable  coils  being  .rigidly  attached  to 
the  same  stem  which  is  suspended  by  a  steel  torsion  wire.  The 
lower  end  of  the  stem  is  centered  by  a  small  steel  pin  which 


12  M. 

_§ 


FIG.  340. — Curve-drawing     polyphase     wattmeter    and     record,    General 

Electric  Co. 

passes  freely  through  a  ring  jewel.  Magnetic  damping  is  em- 
ployed, the  magnets  and  damping  disc  being  just  below  the 
shield.  Strong  non-magnetic  controlling  springs  giving  a  full- 
load  torque  of  500  rnillimeter-grarns  are  used. 

The  pen  consists  of  a  glass  reservoir  containing  a  week's  sup- 
ply of  ink;  into  it  dips  a  capillary  tube  with  an  iridium  tip.     The 


558  ELECTRICAL  MEASUREMENTS 

tip  is  very  hard,  takes  a  high  polish  and  does  not  corrode.  The 
pen  friction  is  thus  reduced.  The  pen  is  carried  by  a  jointed 
arm  attached  to  the  movable  stem.  The  two  members  of  the 
arm  are  nearly  perpendicular  and  the  pen  is  pressed  against  the 
paper  by  a  small  weight  attached  to  a  bell-crank  lever  carried 
by  the  first  member;  the  unweighted  arm  of  the  bell  crank  is 
attached  to  the  second  member  by  a  light  cord. 


FIG.  341. — Pen  and  ink  reservoir  for  General  Electric  Co.  curve-drawing 

meters. 

Relay  Instruments. — The  essential  features  of  a  registering 
relay  wattmeter  for  three-phase  circuits  are  shown  in  Fig.  342. 

The  two  dynamometer  elements  are  shown  at  8  and  9.  The 
spindle  carries  the  outer  end  of  the  flat  spiral  spring,  13,  the  inner 
end  of  which,  15,  is  attached  to  an  arbor  which  is  turned  by  the 
motor  18.  The  motor  is  controlled  by  a  circuit  through  the  relay 
points,  22,  23,  24,  so  that  the  torque  on  the  coil  is  kept  balanced 
by  that  of  the  spring.  The  excursion  of  the  pen  on  the  chart  is 
proportional  to  the  twist  in  the  spring  and  the  resulting  diagram 
is  on  rectangular  coordinates. 

A  relay  voltmeter  is  shown  in  Fig.  343.  The  six  coils  are  ar- 
ranged as  in  the  Kelvin  balance.  The  power  for  moving  the 
pen  is  obtained  from  the  auxiliary  source  B  by  means  of  the 
solenoids  P  and  PI,  one  of  which  moves  the  pen  to  the  right,  the 
other  to  the  left.  The  controlling  spring  S  connects  the  link  M 
and  the  balance  arm,  the  latter  being  provided  with  a  contact 
finger  which  plays  between  the  contacts  at  D.  On  the  passage 
of  the  current  the  finger  is  brought  in  contact  with  the  lower  stop, 
thus  energizing  the  solenoid  P  and  moving  the  pen  to  the  right 
until  the  tension  on  S  is  sufficient  to  break  the  contact;  P  then 
becomes  inactive,  the  linkage  tends  to  return  to  the  zero  position 


GRAPHIC  RECORDING  INSTRUMENTS 


559 


and  the  contact  is  reestablished,  the  result  being  that  the  pen 
remains  practically  stationary  if  the  voltage  be  constant.  If  the 
voltage  falls,  the  upper  contact  and  PI  act  to  bring  the  pen  to  its 
proper  position.  Sparking  at  the  contacts  is  eliminated  by  use 
of  the  condenser  KK  and  the  resistance  R. 


18 1 


FIG.  342. — Elements  of  Arconi  curve-drawing  wattmeter. 


Rectilinear  motion  of  the  pen  is  obtained  by  making  the  arms 
of  the  linkage,  a,  b  and  c  of  equal  length.  The  upper  end  of  c 
slides  in  a  vertical  slot. 

Registering  instruments  are  made  for  both  direct-  and  alter- 
nating-current circuits,  to  measure  current,  voltage,  power, 


560 


ELECTRICAL  MEASUREMENTS 


FIG.  343. — Relay  curve-drawing  voltmeter,  Westinghouse  Co. 


GRAPHIC  RECORDING  INSTRUMENTS          561 

frequency,  and  power  factor.     Special  types  have  been  developed 
for  use  in  tests  of  electric  cars  and  locomotives. 

In  selecting  curve-drawing  instruments  it  should  be  kept  in 
mind  that  in  many  of  those  on  the  market  the  inertia  of  the 
moving  parts  is  so  great  that  rapidly  varying  phenomena  will 
not  be  correctly  depicted. 

References 

"Graphic  Recording  Meters,"  Electric  Journal,  vol.  3,  1906,  p.  296. 

"investigating  Manufacturing  Operations  with  Graphic  Meters,"  C.  W. 
DRAKE,  Electric  Journal,  vol.  7,  1910,  p.  536. 

''A  Graphic  Recording-Ammeter,"  A.  H.  Armstrong,  Trans.  American 
Institute  of  Electrical  Engineers,  Vol.  22.  1903,  page  689. 


36 


CHAPTER  XII 
INSTRUMENT  TRANSFORMERS 

In  the  course  of  development  of  high-voltage  alternating-cur- 
rent systems  of  transmission  and  distribution  it  has  been  found 
necessary  to  remove  the  various  instruments,  as  well  as  the  de- 
vices used  to  actuate  the  switching  gear,  from  direct  contact  with 
the  line  circuits  and  to  operate  them  by  means  of  properly  con- 
structed transformers,  since  direct  connection  between  the  high- 
tension  lines  and  the  devices  on  the  front  of  the  switchboard  must 
be  avoided.  This  method  of  operation  through  transformers  re- 
"duces  to  a  minimum  the  possibility  of  personal  injury  to  the 
station  attendants  and  enables  them,  especially  in  emergencies, 
to  operate  the  apparatus  with  confidence,  thus  contributing  to 
maintaining  continuity  of  the  service. 

Again,  it  is  frequently  necessary  to  meter  very  large  currents 
in  circuits  of  only  moderate  voltage ;  and  as  it  is  highly  desirable 
to  avoid  the  expense  of  carrying  heavy  leads  to  the  switchboard, 
current  transformers  are  used. 

By  properly  choosing  the  transformers,  it  is  possible  to  use  in- 
struments and  switchboard  devices  wound  for  5  amperes  and  1 10 
volts,  for  installations  of  all  capacities.  This  reduces  the  instru- 
ment cost  and  is  now  the  accepted  American  practice. 

Potential  Transformers. — Where  it  is  necessary  to  measure  a 
high  voltage,  a  potential  transformer  is  used  to  reduce  this  vol- 
tage to  a  more  convenient  and  safe  value  for  measurement.  Fig. 
344  shows  two  such  transformers;  they  are  connected  in  the 
circuit  as  shown  in  Fig.  345. 

The  transformer  in  Fig.  345  is  diagrammatic  only;  as  con- 
structed, the  primary  and  secondary  windings  are  superposed. 

As  potential  transformers  are  usually  operated  under  practi- 
cally fixed  conditions  of  applied  voltage,  frequency,  and  number 
and  character  of  the  instruments  in  the  secondary  circuit,  one 
would  expect  them  to  be  instruments  of  precision,  and  experience 

562 


INSTRUMENT  TRANSFORMERS 


563 


shows  this  to  be  the  case.  They  are-much  more  permanent  than 
the  instruments  they  actuate.  When  used  for  voltage  measure- 
ments, only  the  ratio  of  transformation  is  important,  and  this 
should  be  constant  under  the  varying  operating  conditions.  The 
line  voltage  is  given  by 

V  =  (Ratio)  X  (Reading  of  voltmeter). 


* 


•' 


For  2,300-volt  circuit.  For  13,000-volt  circuit. 

FIG.  344. — Potential  transformers,  General  Electric  Co.      Note  stars 
on  base  of  left-hand  transformer  indicating  polarity. 


Load 


FIG.  345. — Showing  manner  of  using  potential  transformer. 

Switchboard  voltmeters  are  graduated  so  that  the  line  voltage 
is  read  directly  from  the  dial.  If  the  ratio  is  not  constant,  the 
combination  of  transformer  and  voltmeter  may  be  calibrated  as 
a  unit. 

Current  Transformers. — The  current  transformer  is  used  in 
cases  where  very  large  alternating  currents  must  be  measured 
and  also  where  the  current  coils  of  instruments  must  be  isolated 
from  high-voltage  lines. 


564 


ELECTRICAL  MEASUREMENTS 


Different  designs  of  this  instrument  are  shown  in  Fig.  346. 

Transformer  A  is  for  use  on  installations  of  from  2,500  to  15,000 
volts.  The  distance  between  the  primary  and  the  secondary 
terminals  and  frame  is  to  be  noted.  Transformer  B  is  a  portable 


B 


FIG.  346. — Current  transformers,  General  Electric  Co. 

instrument  designed  for  general  testing  purposes.  The  ratio  is 
variable,  for  the  primary  is  formed  by  thrusting  a  flexible  cable 
through  the  central  opening,  the  number  of  primary  turns  being 
thus  readily  altered.  Transformer  C  has  its  iron  core  made  in 


INSTRUMENT  TRANSFORMERS  565 

two  parts  which  are  hinged  together  so  that  the  magnetic  circuit 
can  be  opened  when  the  screw  clamp  is  loosened.  This  allows  the 
transformer  to  be  placed  around  a  cable  and  permits  the  current 
in  a  single  conductor  cable  to  be  measured  without  interrupting 
the  service. 

Fig.  347  indicates  the  connections  for  a  simple  current  measure- 
ment. For  obvious  reasons  this  device  is  sometimes  called  a 
series  transformer  in  distinction  from  a  potential  transformer, 
which  is  frequently  called  a  shunt  transformer. 


Load 


FIG.  347. — Showing  manner  of  using  current  transformer. 

For  a  current  measurement, 

/  =  (Ratio)  X  (Reading  of  ammeter). 

Convenience  dictates  that  the  ratio  be  a  constant.  This  involves 
a  difficulty,  for,  as  the  load  changes,  the  transformer  must  work 
under  widely  varying  conditions.  Experiment  shows  that  the 
ratio  is  not  constant,  being  to  a  certain  extent  dependent  on  the 
strength  of  the  current  which  is  being  measured,  and  also  on  the 
number  and  the  character  of  the  instruments  in  the  secondary 
circuit. 

Power  Measurements. — In  power  measurements  on  high- 
voltage  circuits,  it  is  necessary  to  use  both  current  and  potential 
transformers.  As  shown  in  Fig.  348,  the  connections  are  such 
that  the  current  and  voltage  as  well  as  the  power  are  measured. 

With  the  connections  as  shown,  the  power,  to  a  fair  degree  of 
approximation,  is  given  by 

P  =  (Ratio  of  current  transformer)  X  (Ratio  of  potential  trans- 
former) X  (Reading  of  wattmeter). 

Another  difficulty  is  here  encountered.  In  the  discussion  of 
power  measurement,  it  was  repeatedly  emphasized  that  for  ac- 


566 


ELECTRICAL  MEASUREMENTS 


curate  work,  the  currents  in  the  fixed  and  movable  coils  of  a 
dynamometer  wattmeter  must  have  the  same  phase  relation  as 
the  current  and  voltage  of  the  load. 

It  is  one  of  the  imperfections  of  instrument  transformers  that 
they  introduce  false  phase  relations.  With  the  potential  trans- 
former the  voltage  at  the  secondary  terminals  is  not  in  exact 
opposition  to  the  voltage  applied  to  the  primary,  the  departure 
from  exact  opposition  being  small,  to  be  sure,  and  of  the  order 
of  magnitude  of  10'  of  arc  under  normal  operating  conditions. 


Load 


FIG.  348. — Showing  connections  for  measuring  power,  voltage,  and  current, 
using  instrument  transformers. 

This  phase  angle  may  be  either  a  lag  or  a  lead,  and  depends  on 
the  frequency  as  well  as  on  the  number  and  character  of  the  in- 
struments in  the  secondary  circuit. 

The  current  transformer  is  subject  to  a  much  greater  phase- 
angle  error  than  the  potential  transformer.  The  displacement  of 
the  secondary  current  from  exact  opposition  to  that  in  the  pri- 
mary may,  at  low  loads,  sometimes  amount  to  as  much  as  3°. 
This  displacement  depends  on  the  magnitude  of  the  primary  cur- 
rent, on  the  frequency  and  on  the  number  and  the  character  of 
the  instruments  in  the  secondary  circuit. 

It  will  be  seen  that  the  errors  introduced  into  power  measure- 
ment by  the  use  of  transformers  are  those  due  to  the  variation 
of  ratio  of  both  the  current  and  potential  transformers,  as  well 
as  those  due  to  the  phase  displacement  in  both  instruments. 

It  is  possible  to  determine  the  ratio  and  phase  angle  and  to 
make  the  corresponding  correction  so  that  accurate  results  may 
be  obtained  even  at  low  power  factors,  where  the  phase-angle 
errors  are  most  pronounced.  These  matters  are  of  great  prac- 
tical importance,  for  instrument  transformers  are  used  in  con- 


INSTRUMENT  TRANSFORMERS  567 

nection  with  wattmeters  in  all  sorts  of  acceptance  tests  of  alter- 
nating-current apparatus,  as  well  as  in  connection  with  watt-hour 
meters  on  all  high-capacity  alternating-current  circuits. 

General  Considerations. — In  all  instrument  transformers,  the 
primary  must  be  thoroughly  insulated  from  the  secondary  and 
from  the  core  and  case,  so  that  there  is  little  chance  of  punctur- 
ing the  insulation.  In  addition,  the  secondary  circuit  should  be 
grounded  so  that  the  operator  is  protected  even  though  the  in- 
sulation between  the  primary  and  secondary  breaks  down. 
Grounding  the  secondary  circuit  prevents  errors  due  to  accumu- 
lation of  electrostatic  charges  on  the  instruments.  The  coils  must 
be  held  in  place  so  firmly  that  there  is  no  chance  of  mechanical 
injury  when  short-circuits  occur.  The  primary  and  secondary 
terminals  must  be  so  far  apart  that  there  is  no  liability  of  an  arc 
forming  between  the  two  circuits  when  the  line  circuit  is  violently 
disturbed. 

The  ordinary  vector  diagram  for  a  transformer  is  shown  in 
Fig.  349.  It  is  not  drawn  to  scale,  however,  and  gives  no  idea 
of  relative  numerical  magnitudes. 


FIG.  349.  —  Vector  diagram  for  transformer. 

By  means  of  the  diagram,  a  general  explanation  of  the  phe- 

nomena occurring  in  instrument  transformers  may  be  obtained. 

For  the   potential   transformer,   the   ratio   which  is  used  is 


It  differs  in  magnitude  and  in  the  phase  of  its  components  from 

J7 

j^>  which  is  the  ratio  of  the  number  of  turns,  or  the  true  "ratio  of 


568 


ELECTRICAL  MEASUREMENTS 


1.000 


0.991 


34567 
Secondary  Amperes 
(Current  Transformer)  Eatio  Curves 


10 


012 


4567 

Secondary  Amperes 

(Current  Transformer)  Phase  Angle  Curves 


20  14 

12 

-^ 

^ 

20  10 

p 

^5S= 

u* 

_   Oft 

^ 

P 

ss^ 

s^ 

-^ 

bU 

i 

'    - 

~  — 

--~, 

^& 

^ 

02 

- 

--  — 

--•vf 

^ 

^ 

•~—  ^ 

R 

. 

20  00 

^ 

-^ 

^^ 

^"^ 

—  , 

-^ 

— 

-—  . 

•^^ 

, 

~~~~ 

•^. 

W« 

4«x 

/o 

,1 

o' 

'    • 

^ 

L  L. 

n  , 

~-~~ 

-~- 

-~~» 

, 

*•-•. 

•^^. 

^-  —  , 

-^. 

---, 

, 

-^. 

-^^ 

Q'* 

o 

^ 

-^^ 

10 

) 

1 

1 

0 

1 

> 

a 

3 

^ 

3,<, 

T3 

L 

a 

5 

4 

0 

4 

c> 

3 

0 

Potential  Transformer  (Lines  are  for  Non-inductive  Load)  Isolated  Points  R  and  P 
are  Ratio  and  Phase  Angle  Plotted  against  Volt-Amperes  for  20  Per  cent  Power  Factor 


20.16 
.14 
.12 

1-'° 

«.08 
.06 
.04 
.02 

20.00 


Load 


-10 


40          50         60 

ry  Voltage 

Illustrating  the  E.'Cect  of  Change  of  Voltage  upon  Eatio  and  Phase  Angle  of  a 
Potential  Transformer 


90         100        110        120        130       140 
ary  Vol 


INSTRUMENT  TRANSFORMERS  569 

transformation."  The  phase  angle  of  the  potential  transformer  is 
designated  on  the  diagram  by  7.  This  angle  is  the  departure 
from  exact  opposition  of  Fi  and  F2.  It  is  usually  very  small  and 
in  reality  may  be  either  an  angle  of  lead  or  of  lag,  according  to 
circumstances.  The  phase  angle  of  the  current  transformer  will 
be  denoted  by  |8. 

Fig.  350  shows  the  results  of  experimental  determinations  of 
the  constants  of  certain  commercial  current  and  potential  trans- 
formers. It  gives  an  idea  of  the  order  of  magnitude  of  the 
changes  to  which  the  ratios  and  phase  angles  are  subject. 
Similar  curves,  giving  representative  values  of  ratios  and 
phase  angles,  which  have  been  determined  by  testing  a  few 
transformers  all  made  in  accordance  with  the  same  specifications, 
may  be  obtained  from  the  makers  of  such  instruments  and  are 
sufficiently  accurate  for  much  commercial  work. 

In  tests  where  the  greatest  accuracy  is  desired,  the  ratios  and 
phase  angles  for  the  transformers  should  be  determined  at  the 
frequency  and  voltage  and  with  the  same  connected  burden  of 
instruments  and  leads  as  are  to  be  used  in  the  subsequent  work. 


C 

FIG.  351.  —  Pertaining  to  polarity  tests  of  instrument  transformers. 

When  using  instrument  transformers  in  connection  with  watt- 
meters and  power-factor  meters  it  is  necessary  to  know  the  rela- 
tive polarities  of  the  secondaries  of  the  transformers  with  respect 
to  their  primaries,  otherwise  the  meters  may  be  so  connected  that 
they  will  not  read  properly. 

Some  manufacturers  arrange  the  internal  connections  so  that 
the  corresponding  terminals  of  the  primary  and  of  the  secondary 


570  ELECTRICAL  MEASUREMENTS 

are  always  of  like  polarity.  Thus  in  Fig.  351 A  the  +  and  — 
signs  indicate  the  polarities  at  some  particular  instant.  The 
primary  and  secondary  currents  are  shown  diagrammatically  as 
flowing  in  opposite  directions. 

The  +  on  the  primary  is  the  terminal  at  which  the  cur- 
rent enters  and  the  +  on  the  secondary  is  the  terminal  by 
which  the  current  leaves  the  transformer  to  enter  the  external 
circuit. 

Some  manufacturers  cross  the  secondary  connections  giving 
the  relative  polarity  shown  in  Fig.  35 IB. 

A  simple  method  of  testing  the  polarity  is  as  follows :  connect 
a  direct-current  voltmeter  to  one  of  the  windings  (Fig.  35 1C) 
noting  which  terminal  is  connected  to  the  +  post  of  the  volt- 
meter. Touch  for  an  instant  the  terminals  of  a  dry  cell  to  the 
terminals  of  the  other  winding,  making  the  polarity  such  that 
the  meter  reads  up  the  scale  on  closing  the  circuit.  The  two  cor- 
responding +  terminals  will  be  the  carbon  of  the  cell  and  the 
+  post  of  the  voltmeter.  A  very  small  current  should  be  used, 
otherwise  the  iron  may  be  left  in  a  highly  magnetized  condition 
and  the  ratio  and  the  phase  angle  of  the  transformer  altered  from 
their  normal  values. 

When  stating  the  conditions  under  which  instrument  trans- 
formers are  used  (especially  current  transformers)  it  is  highly 
desirable  that  the  inductance  and  resistance  of  the  external  sec- 
ondary circuits  be  specified,  for  in  that  case  there  can  be  no  mis- 
understanding of  the  conditions  under  which  the  transformer  is 
operating. 

If  the  conditions  are  such  that  the  readings  of  the  5-ampere 
wattmeters  and  ammeters,  which  are  commonly  used  in  the  sec- 
ondary circuits  of  current  transformers,  are  in  the  lower  parts  of 
the  scales  there  is  a  temptation  to  substitute  lower  range  instru- 
ments (for  instance,  3  amperes)  in  order  to  obtain  a  good  scale 
reading.  It  must  not  be  forgotten  that  such  instruments  will 
heavily  tax  the  current  transformer  and  alter  both  the  ratio  and 
the  phase  angle,  for  the  burden  placed  on  the  transformer  by  the 
3-ampere  equipment  is  such  that  the  voltage  at  the  transformer 
terminals  must  be  increased  to  approximately  2. 8  times  its  original 
value. 


INSTRUMENT  TRANSFORMERS 


571 


RESISTANCE  AND  INDUCTANCE  OF  THE  CURRENT  COILS  OF  TYPICAL  ALTER- 
NATING-CURRENT INSTRUMENTS 


Range 

Ammeters 

Wattmeters 

Resistance 

Inductance 

Resistance 

Inductance 

3  amp. 

0.37  ohm 

0.00076  henry 

0.36  ohm 

0.00046  henry 

5  amp. 

0.133  ohm 

0.00028  henry 

0.119  ohm 

0.00016  henry 

Current  Transformers. — It  is  important  that  when  the  trans- 
former is  being  operated  the  secondary  circuit  always  be  kept 
closed.  If  it  is  opened,  there  will  be  no  demagnetizing  effect 
due  to  the  secondary,  and  as  the  primary  current  is  fixed  by  the 
load  on  the  line,  the  flux  will  rise  to  a  high  value.  This  will 
increase  the  iron  losses  to  such  an  extent  that  the  insulation  may 
be  injured  by  the  heat  so  that  at  some  subsequent  time  it  may 
be  punctured  by  a  moderate  voltage,  or  perhaps  burned  out. 
Again,  the  voltage  at  the  secondary  terminals  will  be  large,  and 
the  secondary  insulation  may  be  injured.  There  is  also  the  possi- 
bility of  disagreeable,  if  not  fatal,  shocks. 

Opening  the  secondary  circuit  when  the  transformer  is  being 
operated  may  alter  both  the  ratio  and  the  phase  angle,  for  the 
circuit  opening  may  occur  when  the  iron  is  fully  magnetized.  In 
the  subsequent  use  of  the  instrument,  the  iron  will  not  be  put 
through  its  normal  hysteresis  cycle,  and  the  exciting  current  will 
therefore  be  altered.  At  low  loads,  the  alteration  may  amount 
to  several  per  cent.  For  the  same  reason,  direct  current,  used 
for  the  purpose  of  calibrating  the  instruments,  must  never  be 
sent  through  either  the  primary  or  secondary  of  the  transformer. 
Under  ordinary  operating  conditions,  these  changes  in  the  mag- 
netic state  of  the  core  will  persist,  since,  in  instrument  trans- 
formers, the  magnetic  circuit  is  unusually  good.  The  core  may 
be  demagnetized  in  the  usual  manner,  an  alternating  current 
being  sent  through  the  primary,  and  gradually  decreased  from 
its  full-load  value  to  zero,  the  secondary  being  open. 

Owing  to  the  necessity  of  having  considerable  insulation  be- 
tween the  primary  and  the  secondary  coils  and  of  having  the 
terminals  of  the  coils  widely  separated  there  may  be  a  pronounced 
stray  field  in  the  neighborhood  of  current  transformers.  This  is 
the  case  with  the  type  shown  in  Fig.  346A.  Instruments,  if  not 


572 


ELECTRICAL  MEASUREMENTS 


shielded,  should  be  used  at  a  distance  of  at  least  6  or  8  ft.  from  the 
transformer. 

Theory  of  the  Current  Transformer. — To  examine  the  theory 
of  the  current  transformer,  transfer  from  Fig.  349  those  parts  of 
the  diagram  which  are  shown  in  Fig.  352. 


FIG.  352. — Diagram  for  current  transformer. 
Let: 

Ni  and  Nz  =  number  of  turns  in  primary  and  secondary  respectively 
Ii    and  7  2    =  primary  and  secondary  currents. 

7o   =  total  exciting  current. 

IM  =  magnetizing  component  of  exciting  current. 

IP  =  power  component  of  exciting  current. 

6'    =  angle  between  E*  and  secondary  current. 

/3     =  phase  angle  of  transformer. 

Reference  to  the  figure  will  show  that  both  the  ratio  and  the 
phase  angle  are  dependent  on  the  exciting  current,  for  obviously 
if  /o  were  zero,  IiNi  =  IzNz,  and  f$,  the  phase  angle  of  the  trans- 
former or  the  departure  of  the  primary  and  secondary  currents 
from  exact  opposition,  would  also  become  zero.  Such  an  ideal 
transformer  can  never  be  realized,  for  in  any  case  there  must  be 
enough  ampere-turns  to  give  the  requisite  flux  through  the  core, 
and  with  the  iron  core,  the  exciting  current  must  have  an  energy 
component  sufficient  to  account  for  the  hysteresis  and  the  eddy- 
current  losses.  When  an  iron  core  is  used,  loNi  may  be  resolved 
into  two  components,  the  magnetizing  component  IMNi  along 
the  flux,  and  the  power  component  IPNi  along  E\. 

Referring  to  Fig.  352  and  projecting  I2NZ  and  loNi  on  the  line 


/i 

/2 


=  N2I2  cos  |8  +  loNi  cos  ^90  -  0'  - 


L 

IM  sin  (Br  +  j8)  +  IP  cos  (Bf  + 

/2 


0) 


(a) 


INSTRUMENT  TRANSFORMERS  573 

But  0  is  a  small  angle;  its  cosine  is,  therefore,  very  nearly  unity, 
and  the  second  member  on  the  right-hand  side  of  the  equation 
is  virtually  a  correction  term. 
Hence: 

_   ..         7i       N2   ,    IM  sin  0'  +  IP  cos  0' 
Ratio  =  T~  —  "vT  H —  ~~r —  ~  approximately. 

1%       JM  i  1 2 

The  expression  for  the  phase  angle  is  determined  as  follows. 
From  the  diagram, 


o#i  sin  [90  -  6f  -  |8  -  sin-1  ^ 


tan  B  = 

1ZJ\2  COS  ft 
T..\T,   n/^c   fa'  _L  R\    —    T-  AT.  sm   (Qf  _f_  fl) 

— .      (6) 


1  2-/V  2  COS  p 

As  jS  is  a  small  angle, 

f  cos  0'  —  IP  sin  0'~i 

—= —  approximately. 

-/  2  J 

In  the  practical  case  72  leads  7i  reversed.  This  is  important 
in  power  measurements. 

The  dependence  of  the  ratio  and  the  phase  angle  on  the  proper- 
ties of  the  core  are  clearly  shown  in  (a)  and  (6).  Evidently  both 
IM  and  IP  should  be  reduced  to  a  minimum  if  both  the  ratio  and 
the  phase  angle  are  to  be  made  as  nearly  independent  of  the 
secondary  current  and  the  character  of  the  secondary  load  as 
possible. 

In  the  current  transformer  70  varies  with  the  saturation  of  the 
core,  i.  e.,  with  consumers'  load  current.  To  reduce  IM  the  core 
must  be  of  high  permeability  and  of  large  cross-section.  IP  is 
rendered  small  by  choosing  for  the  core  an  iron  of  small  hysteresis 
loss  and  working  the  iron  at  a  very  low  flux  density.  The  im- 
pedance of  the  instruments  forming  the  load  should  be  small  so 
that  the  requisite  secondary  e.m.f.  is  furnished  by  a  small  flux. 

As  there  is  iron  in  the  magnetic  circuit  the  current  wave  form 
in  the  secondary  cannot  be  an  exact  reproduction  of  that  in  the 
primary.  But  with  periodic  phenomena  the  distortion,  while 
measurable  by  refined  methods,  is  so  small  that  it  is  of  no  prac- 
tical moment  even  though  the  wave  form  be  very  complicated. 

Owing  to  the  action  of  the  iron,  however,  large  currents  of  a 
transient  nature,  such  as  occur  in  short-circuit  tests  of  fuses. 


574 


ELECTRICAL  MEASUREMENTS 


switches,  etc.,  and  which  rise  to  values  much  higher  than  those  for 
which  the  transformer  was  designed  are  not  correctly  reproduced. 
Fig.  353  shows  the  results  of  measurements  of  the  magnetizing 
and  the  power  components  of  the  exciting  current,  /o,  made  by 
use  of  a  quadrature  dynamometer.13  The  tests  were  made  at  25 
and  60  cycles  on  the  current  transformer  to  which  the  data 


-at  25  Cycles  per  Second 
at  60  Cycles  per  Second 


20  40 

%  Bated  Full  Load  Current 

FIG.    353. — Showing    components    of    total    exciting    current   in    current 

transformer. 

given  below  apply,  and  Fig.  354  shows  how  well  calculations 
based  on  these  results  agree  with  direct  measurements  of  the 
ratio  and  phase  angle. 

In  order  to  give  an  idea  of  the  magnitude  of  the  quantities 
involved,  reference  may  be  made  to  the  following  data  which 
pertain  to  the  current  transformer  whose  characteristics  are  given 
in  Figs.  353  and  354: 

/        8 

Nominal  ratio  =   ~  =  -• 
LI       1 

Primary  turns  =  JVi  =  25. 
Secondary  turns  =  N2  =  196. 


INSTRUMENT  TRANSFORMERS 


575 


Rated  full-load  currents  of  primary  and  secondary,  40  and  5 
amp.,  respectively. 

Secondary  resistance,  0.51  ohm. 
Resistance  of  connected  load,  0.17  ohm. 
Inductance  of  connected  load,  0.08  millihenry. 
Max.  flux  density  at  60  cycles,  290  gausses. 
Max.  flux  density  at  25  cycles,  700  gausses. 


0 

tS  101.5 
a  101.0 

a 

*  100.5 

100.0 
( 

x  Computed  Points 
o  Observed  Points 

>"""""1 

r: 

>,  * 

- 

—              —  ^ 

— 

_GO~ 

J                     20                    40                     GO                    80                    100 

%  Rated  Full  Load  Sec.  Amps. 


ZDU 

200 

\ 

\ 

. 

x  Computed  Points 

_        / 

• 

^ 

o  Observed  Points 

I1'" 

s 

^v^ 

•<       ' 

V 

"V- 

-^.^^ 

1 

1 

^^, 

f  —  •  —  . 

1  ^ 

!  —  ^ 

PH       ' 

^^ 

9^ 

50 

^                 • 

^  -^. 

— 

^            — 

^           ; 

0  20  40  GO  80  100 

%  Rated  Full  Load  Sec.  Amps. 

FIG.  354. — Showing  agreement  of  computed  and  observed  values  of  the 
ratio  and  phase  angle  of  a  current  transformer.  The  form  of  the  ratio  curve 
is  abnormal;  the  ratio  usually  decreases  with  increase  of  load. 

It  will  be  noted  that  in  order  to  bring  the  ratio  to  its  rated 
value  a  few  secondary  turns  are  left  off.  Attention  is  called  to 
the  low  flux  densities  at  which  the  core  is  worked. 

Theory  of  Potential  Transformer. — In  the  theory  of  the 
potential  transformer  the  two  most  important  quantities  are  the 
equivalent  reactance  and  resistance  as  determined  by  the  usual 
short-circuit  test.  The  exciting  current  and  the  reactance  and 
resistance  of  the  primary  windings  must  also  be  taken  into  ac- 
count but  their  combined  influence  is  much  less  than  that  of  the 
equivalent  impedance. 


576  ELECTRICAL  MEASUREMENTS 

Referring  to  Fig.  355, 
Let: 

Ni  and  TV  2  =  number  of  primary  and  secondary  turns,  respectively. 

R  and  X  =  equivalent  resistance  and  reactance  of  the  transformer. 

Ri  and  Xi  =  resistance  and  reactance  of  the  primary  windings. 

/o  =  exciting  current. 

Vi  and  V-z  =  primary  and  secondary  terminal  voltages. 

0  =  power  factor  angle  of  the  secondary  load. 

5  =  angle  between  /o  and  Vz  reversed. 

7  =  phase  angle  of  the  transformer,  or  the  angle  between  Fi  and  F2. 


FIG.  355.  —  Diagram  for  potential  transformer. 

The  component  of  the  primary  current  which  is  in  opposition 
to  the  secondary  current  is  1  2  TT~  =  /.     To  determine  the  ratio, 

projecting  V\  on  F2  and  adding  up  the  components  of  the  projec- 
tion, gives, 

Fi  cos  7  =  F2  ^  +  IR  cos  0  +  IX  sin  0  +  I0Ri  cos  5  +  I0X1  sin  8. 

J\2 

#!      7^cos^  +  /^sin(9  +  /o^icos6  +  /o^]  sing"[ 

F2 


In  potential  transformers  7  is  usually  considerably  less  than 
1°,  so  cos  7  =  1  very  closely,  and 

Fi  _  Ni      IR  cos  9  +  IX  sin  6  +  I0Ri  cos  5  +  70^i    sin  5 
7*  ~  AV.."1  F8 

To  determine  the  phase  angle,  projecting  on  a  line  perpendicu- 
lar to  F2,  gives 

FI  sin  7  =  IR  sin  0  —  IX  cos  0  +  I0Ri  sin  5  —  loXi  cos  5 
but  for  small  angles  sin  7  =  7  approximately,  so 

7  =  y  \IR  sin  0  —  IX  cos  6  +  /o-Ri  sin  6  —  /o^Ti  cos  5  I 

In  the  potential  transformer  the  small  change  of  exciting  cur- 
rent, /o,  between  no-load  and  full-load  produces  a  negligible 
effect  on  the  results. 


INSTRUMENT  TRANSFORMERS  577 

Application  of  Corrections  for  Ratio  and  Phase  Angle. — It  is 

customary  to  express  the  results  of  tests  of  instrument  trans- 
formers in  the  form  of  curves  similar  to  those  in  Fig.  350.  Ref- 
erence to  the  curves  having  the  proper  load  characteristics  will 
give  the  ratio  and  phase  angle  to  be  used  in  any  particular  tests. 
When  power  measurements  are  made,  besides  the  ratios,  there 
are  to  be  considered : 

1.  The  phase  displacement  in  the  potential  transformer. 

2.  The  phase  displacement  in  the  current  transformer. 

3.  The  phase  displacement  in  the  potential  coil  of  the  watt- 
meter. 

These  phase  relations  may  be  indicated  as  in  Fig.  356. 


Vz  at_Sec.ot  Poten.Trans. 

Applied  to 

Load 
f  °ie":0'«  Of 


FIG.  356. — Phase    diagram    for    power    measurement    using    instrument 

transformers. 

The  phase  angle,  7,  of  the  potential  transformer  is  shown  as  a 
lead,  though  V%  may  either  lag  behind  or  lead  Vi  according  to  cir- 
cumstances. If  7  is  a  lag  angle,  its  algebraic  sign  is  to  be  reversed. 

The  wattmeter  gives  an  indication  proportional  to  the  mean 
product  of  the  current  in  its  two  coils,  or  to  cos  0'.  The  apparent 
power  factor  of  the  load  is 

.,       Wattmeter  reading 
cos  6'  =  — Tr  ..  — . 

Volt-amperes 

The  true  power-factor  angle  is 

e  =  B'  +  ft  +  eP  -  7 

and  the  true  power  factor  is 

True  watts 
cos  6  =  cos  (0'  +  0  +  Op  -  7)  = 


Volt-amperes 
.'.  True  watts  =      —,  X  (wattmeter  reading)  = 

[1  —  tan  6'  tan  (0  +  0P  —  7)]  X  (Reading), approximately. 

37 


578  ELECTRICAL  MEASUREMENTS 

The  true  watts  must  be  multiplied  by  the  appropriate  trans- 
former ratios  to  give  the  power  in  the* circuit.  Obviously,  the 
effect  of  the  phase  angles  increases  as  the  power  factor  of  the 
load  decreases. 

To  illustrate  the  foregoing,  consider  the  following  data: 

The  losses  in  the  instruments  are  neglected. 

Inductive  load,  25  cycles. 

Reading  of  ammeter,  corrected  for  calibration,  1.5  amp. 

Reading  of  voltmeter,  corrected  for  calibration,  110.5  volts. 

Reading  of  wattmeter,  corrected  for  calibration,  50.0  watts. 

dp  is  negligible. 

Nominal  ratio  of  current  transformer,  8:1. 

Ratio  of  current  transformer  from  its  curve,  1.0125  X  8. 

Phase  angle  /3,  from  current  transformer  curve,  1°.79. 

Nominal  ratio  of  potential  transformer,  10  : 1. 

Ratio  of  potential  transformer  from  its  curve,  0.995  X  10. 

Phase  angle  7  from  potential  transformer  curve,  0°.12. 

F2  lags  behind  —  Vi. 

Apparent  power  factor  =  cos  6'  =  1 1 A  ,       1  ,  =  0.3016. 

Ilu.o  X  JU.O 

Apparent  power-factor  angle,  72°.45. 

True  power-factor  angle  =  6  =  72°.45  +  1°.79  +  0°.12  =  74°.36. 

True  power  factor  =  cos  9  =  0.2696. 

n  *?fiQfi 
True  value  of  the  load  =  ~     ^  X  50  X  8.1  X  9.95  =  3,602  watts, 

U.oUlO 

which  is  the  corrected  reading  of  the  wattmeter  multiplied  by 
the  proper  transformer  ratios. 

Effect  of  Phase  Angles  in  Three-phase  Power  Measurements. 
—The  case  which  will  be  considered  is  that  of  a  balanced  three- 
phase  load  where  the  power  is  measured  by  the  two-wattmeter 
method  using  transformers  of  the  same  characteristics  in  both 
phases.  When  the  power  factor  of  the  load  is  low  the  watt- 
meter, in  the  coils  of  which  the  currents  are  the  more  nearly  in 
phase,  indicates  the  larger  part  of  the  load.  The  reading  of  the 
other  wattmeter,  which  works  under  much  more  adverse  condi- 
tions as  to  the  phase  displacement  of  the  currents  in  its  coils,  is 
small  so  that  even  if  the  percentage  error  in  its  readings  be  large, 
the  percentage  error  introduced  by  it  into  the  measurement  of 
the  power  will  be  small. 


INSTRUMENT  TRANSFORMERS  579 

It  has  just  been  shown  that  the  power  in  a  single-phase  circuit 
is  given  by 

cos  6 


Assume  that  the  transformer  ratios  are  1:1,  then  in  the  two- 
wattmeter  method  the  power  which  should  be  indicated  by  the 
two  instruments  is 

Pl  =  VI  cos  (30°  +  8). 

P2  =  VI  cos  (30°  -  0). 
So 

P  =  F7[cos  (30°  +  0)  +  cos  (30°  -  0)]  =VlV%  cos  0. 

The  effect  of  the  phase  angles  of  the  transformers  and  that  of 
the  potential  circuit  of  the  wattmeter  is  to  reduce  the  phase  dif- 
ference of  the  currents  in  the  fixed  and  movable  coils  of  the  watt- 
meters by  the  angle  ft  +  8P  —  7;  the  readings  become: 
(Reading)!  =  VI  cos  [30°  +  0  -  0  -  0P  +  7]  =  VI  cos  [30°  +  0']. 
(Reading)  2  =  VI  cos  [30°  -  0  +  0  +  Op  -  y]  =  VI  cos  [30°  -  0']. 

(Reading  of  meters)  =  VI  \/3  cos  6'. 

,_.      ,.     N  cos  0 
So  P  =  (Reading)  --  -. 
cos  0 

That  is,  the  fractional  error  due  to  the  phase  angles  is  the  same 
as  that  occurring  in  a  single-phase  measurement  at  the  same 
power  factor. 

If  the  load  is  not  balanced  the  readings  of  each  instrument 
should  be  corrected  as  in  a  single-phase  measurement. 

Use  of  Transformers  with  Watt  -hour  Meters.  —  It  is  customary 
to  use  instrument  transformers  in  connection  with  induction 
watt-hour  meters.  In  this  case,  especially  at  low  power  factors, 
an  additional  complication  is  introduced,  for  both  the  phase 
angles  of  the  transformers  and  the  adjustments  of  the  phase 
relations  of  the  fluxes  in  the  potential  circuits  of  the  meters 
affect  the  measurements. 

To  be  ideally  perfect  an  induction  meter,  when  used  with  a 
current  transformer,  would  have  to  be  lagged  so  that  the  time- 
phase  angle  between  the  potential  coil  flux  and  the  current  in 
the  secondary  of  the  current  transformer  plus  the  power-factor 
angle  of  the  load  would  be  90°.  This  suggests  that  the  watt- 
hour  meter  and  the  transformers  be  treated  as  a  unit  when  the 


580 


ELECTRICAL  MEASUREMENTS 


lag  adjustment  is  made.  However,  a  perfect  adjustment  is  not 
possible,  for  both  the  ratios  and  the  phase  angles  vary  with  the 
load. 

In  careful  industrial  tests,  the  combination  of  watt-hour  meter 
and  instrument  transformers  may  be  calibrated  in  the  laboratory 
without  undue  expenditure  of  power  by  using  fictitious  loads 
(see  page  500).  The  test  conditions  may  then  be  reproduced, 
wave  form  excepted. 

An  attempt  is  sometimes  made  to  correct  for  the  variation  of 
the  ratio  of  the  current  transformer,  which  is  most  troublesome 
at  light  loads,  by  altering  the  light-load  adjustment  of  the  meter. 
If  the  ratio  increases  at  the  light  loads  the  adjustment  is  set  so 
that  the  meter  runs  a  little  fast,  creeping  being  avoided.  There 
is  no  means  of  making  even  an  approximate  adjustment  for  the 
variation  of  the  phase  angle. 


DETERMINATION  OF  THE  RATIOS  AND  PHASE  ANGLES  OF 
INSTRUMENT  TRANSFORMERS 

From  what  has  preceded  it  is  evident  that  if  accurate  measure- 
ments are  to  be  made,  it  is  necessary  to  know  both  the  ratios  and 
the  phase  angles  of  the  transformers.  Among  the  various  meth- 
ods which  have  been  devised  for  their  determination,  a  few  of 
those  based  on  the  potentiometer  principle  have  become  gener- 
ally accepted  as  being  the  best.  They  give  results  of  high 

/, accuracy  and  are  convenient 

because  they  do  not  require 
currents  and  voltages  to  be 
held  at  fixed  values. 

Ratio  and  Phase  Angle  of 
Current     Transformer. — The 
determination  of  the  ratio  of 
FIG.  357. — Connections  for  determining    a  current  transformer  is  sim- 

ply  the  determination  of  the 

ratio   of  two   currents.      To   make  such  a  measurement  using 
direct  currents  the  connections  shown  in  Fig.  357  are  used. 
If  the  detector  stands  at  zero, 


To  Source  of 


To  Detector 


To  Source  of  /2 


/I 

/2 


Ri 


INSTRUMENT  TRANSFORMERS  581 

When  two  alternating  currents  are  to  be  compared,  the  re- 
sistances Ri  and  Rz  should  be  non-inductive;  I\  and  72  must  have 
the  same  frequency  and  wave  form  and  either  be  in  time  phase 
or  have  a  fixed  phase  difference. 

In  applying  this  general  method  to  the  testing  of  current  trans- 
formers, /i  and  72  are  the  currents  in  the  primary  and  secondary 
circuits;  they  will  ordinarily  be  in  phase  to  within  2°  or  less.  As 
this  time-phase  difference  exists,  it  is  impossible  by  any  adjust- 
ment of  the  resistances  R i  and  R2  to  balance  the  two  IR  drops. 

In  order  to  bring  the  detector  to  zero,  unless  it  be  separately 
excited,  it  is  convenient  to  inject  into  the  detector  circuit  an 
e.m.f.  in  quadrature  with  72.  This  may  be  done  by  the  method 

Current  Trans. 

-_P_  Ii  e          Rl        a 


Detector 


m 

Aoun7ter  Variable  Mutual 

Inductance 

FIG.  358. — Connection  for  determining  characteristics  of  current    trans- 
formers. 

• 

used  by  Hughes  and  by  Heaviside  in  their  inductance  bridges,  by 
employing  a  variable  mutual  inductance,  or  air-core  trans- 
former, m,  see  Fig.  358. 

The  arrangement  of  apparatus  shown  diagrammatically  in 
Fig.  358  has  been  used  by  a  number  of  experimenters,  the  chief 
differences  being  in  the  form  and  manner  of  using  the  detector. 

Sharp  and  Crawford  use  a  D'Arsonval  galvanometer,  the 
current  being  rectified  by  a  synchronous  reversing  key  driven  by  a 
synchronous  motor.  The  brushes  or  their  equivalent  are  so 
mounted  that  the  time  phase  of  the  commutation  may  be  altered, 
for  it  must  be  matched  with  the  time  phase  of  the  potential 
difference  between  a  and  b. 

Agnew  and  Silsbee  use  a  vibration  galvanometer  of  special 
design. 

Let  the  circuits  be  as  in  Fig.  359. 

Then   by  a  double   adjustment   of  R2  and  m  the  vibration 
galvanometer  may  be  brought  to  zero. 


582 


ELECTRICAL  MEASUREMENTS 


Using  the  mesh  currents  as  indicated, 

IG  (Z,  +  ZG  +  Z2)  -  XZ,  -  YZ2  +  JcomF  =  0 
XZ,  +  YZ*  -  j 


At  balance  I0  =  0  or 

XZl  +  FZ2 

In  this  case  X  =  —  7i,  Y  =  72, 
also 

Z,  =  #, 


FIG.  359.  —  Mesh  diagram  for  Fig.   358,   pertaining  to  determination   of 
characteristics  of  current  transformers. 


Substituting, 


-\ 


T 


The   value  of  /i2  in  terms  of  722  and  the  constants  of  the 
circuit  is 
j  2  =  rfliW  +  co2L!2fl?2       co2^!2  (L2-m)2+co4L!2  (L2-m)21     2 

"  I   (/e^  +  co2/^2)2  (#i2+co2L!2)2  .  J  2' 

Ratio  = 


1  +  oj2(L2-m) 


co2(L2 


2/7".. 


i    T  7-  , 

leads  /!  by  tan 


/I  ^2 

.'.  ~-  =  —  approximately. 

>L}Rz  —  co^i  (Z/2  — 


INSTRUMENT  TRANSFORMERS 


583 


Naturally  the  inductances  LI  and  L2  are  made  as  small  as 
possible;  if  they  could  be  entirely  neglected, 


tan  j8  = 


com 


The  same  results  may  be  more  simply  derived  by  use  of  a  vec- 
tor diagram,  Fig.  360.  Take  72  along  the  horizontal  axis,  and 
assume  that  the  condition  of  balance  has  been  attained. 


FIG.  360.  —  Vector  diagram  for  Fig.  358. 

At  balance  the  P.D.ea  must  equal  the  P.D.dc  (see  Fig.  358); 
that  is,  the  points  a  and  c  in  Fig.  360  must  coincide;  so 


co2(L2-m) 


When  a  and  c  coincide, 

tan  ]S  =  tan  (a  +  5). 

co  (L2  —  m) 
tan  a  = — -       —A 


tan  8  =   ^=- 

_  co  (Z/2  —  m) 
tan  B  =- 


1  + 


co2  (L2  -  m) 


(L2  -  m) 


With  good  transformers  the  quantity  m  is  small;  both  RI  and  R2 
are  non-inductive,  so  called.  Though  reduced  to  a  minimum,  Z/i 
and  L2  may  be  of  importance  when  phase  angles  are  determined. 


584 


ELECTRICAL  MEASUREMENTS 


A  variable  mutual  inductance  designed  for  this  measurement  is 
shown  in  Fig.  205,  page  346. 

The  arrangement  shown  in  Fig.  358  is  an  alternating  current 
potentiometer  of  limited  range.  The  underlying  idea  may  be 
developed  so  that  an  instrument  generally  applicable  to  measure- 
ments with  sinusoidal  currents  results. 

Ratio  and  Phase  Angle  of  Potential  Transformers. — The  ratio 
of  a  potential  transformer  for  moderate  voltages  may  be  deter- 
mined by  voltmeter  measurements  using  two  similar  instruments, 
one  of  them  being  supplied  with  the  proper  multiplier,  so  that 
the  readings  of  the  two  voltmeters  do  not  differ  greatly.  In  this 
case  uncalibrated  instruments  may  be  used. 


Transformer  Under 
Test 


FIG.  361. — Pertaining  to  determination  of  ratios  of  potential  transformers  by 

voltmeters. 

It  is  frequently  convenient  to  use  a  second  potential  trans- 
former, as  shown  in  Fig.  361,  to  raise  the  ordinary  supply  vol- 
tage to  that  required  for  the  test.  The  total  resistances  of  the 
voltmeter  circuits  are  RP  and  Rs. 

Two  sets  of  readings  are  made,  the  first  with  the  connections 
as  shown;  call  the  readings,  in  volts,  of  the  primary  and  secondary 
instruments,  DP  and  Ds. 

.  A  second  set  of  readings  is  made  after  putting  the  two  volt- 
meters in  series  and  bringing  the  indications  up  to  DP  and  Ds, 
as  nearly  as  is  practicable.  If  .the  multiplier  is  large,  this  is  ac- 
complished sufficiently  well  by  placing  the  secondary  voltmeter 
in  the  primary  circuit,  in  series  with  the  other  instrument  and  its 
multiplier.  During  the  second  set  of  readings,  the  same  current 
flows  through  both  instruments.  Call  the  readings,  in  volts,  D'P 

and  D's  and  the  current  7;.then  yr>-  and  -^-f-  are  the  currents 

Up  Lf  s 

per  scale  unit  of  the  two  instruments. 


INSTRUMENT  TRANSFORMERS  585 

In  the  first  case, 

v.  -  if,*, 

and 

/ 

So 


With  a  slight  modification,  Poggendorf s  method  of  comparing 
an  e.m.f.  and  a  P.D.  may  be  applied  to  the  determination  of  the 
voltage  ratios  and  phase  angles  of  potential  transformers. 

For  comparing  two  direct  potentials  the  connections  shown  in 
Fig.  362  may  be  used. 


FIG.  362.  —  Connections  for  determining  the  ratio  of  a  direct  current  P.  D. 
to  a  direct  current  e.m.f. 

If  the  detector  stands  at  zero, 


In  testing  potential  transformers,  Vi  and  F2  are  replaced  by 
the  primary  and  secondary  terminal  voltages,  and  either  Ri  or 
R2  must  contain  an  adjustable  reactor  by  which  the  P.D.  across 
Rz  may  be  brought  into  time  phase  with  F2.  This  is  necessary 
on  account  of  the  phase  angle  of  the  transformer.  If  the  adjust- 
able reactor  were  not  used,  the  detector  could  be  brought  to  a 
minimum  but  not  to  zero. 

Except  as  mentioned,  the  resistances  should  be  non-reactive, 
that  is,  free  from  both  inductance  and  capacity  effects.  With 
very  high  voltages  it  may  be  necessary  to  use  shielded  resist- 
ances21 to  avoid  the  last.  Either  R\  or  J?2  must  be  adjustable. 
The  detector  may  well  be  a  vibration  galvanometer. 

The  connections  for  the  potential  transformer  test  are  shown 
in  Fig.  363. 


586 


ELECTRICAL  MEASUREMENTS 


To  find  the  condition  of  balance,  the  mesh  equations  are 

X(Zi  +  Z2)  --  YZ2  +Vi  =  Q 

Y(ZG  +  Z2) 

The  galvanometer  current  is 

y     = 

- 


Z6(ZL  +  Z2)  +  Z,£2- 

In  this,  as  in  other  similar  cases  involving  networks,  the  equa- 
tion for  Y  might  have  been  written  at  once  from  the  solution  for 
the  direct-current  case,  simply  replacing  the  resistances  by  im- 
pedances in  the  vector  notation. 


Load 


FIG.  363.  —  Connections  for  determining  characteristics  of  potential  trans- 

formers. 


For  balance,  I0  =  Y  =  0  and 


Let  Zi  be  without  reactance,  then, 


Z2  must  then  be  reactive,  so 

Z2  =  Rz  +  jcoZ/2 
*)  +jcoL 


T/  i 

~  L 

r(fii  +/g2)(^2  -JM          T/ 
J?22+co2L22   ' 


-| 
J  V 


The  value  of  TV  in  terms  of  F22  and  the  constants  of  the 
circuit  is 


v  2  =  r^1 

"     L 


,  ^22co2L22  +  co4L24n      2 

^22  +    «2Ls82    J 


INSTRUMENT  TRANSFORMERS  587 

17. 

Ratio 


io- FI-     / 

l°     72     V 


approximately, 
leads  Vi,  and  tan  7  =    p  /p    "-^r- 


/LI  -f-  R  2 


2L 


As  the  phase  angle  may  be  either  positive  or  negative,  it  is 
necessary  to  be  able  to  give  Z2  either  a  positive  or  negative  reac- 
tance. This  may  be  accomplished  if  it  is  made  up  as  shown  in 
Fig.  364.  The  condenser  C2  is  shunted  by  a  variable  non-induct- 
ive resistance  r2;  L2  is  an  inductance, 


,  =  R,  -  Pl 


FIG.  364. — Arrangement  for  obtaining  positive  and  negative  reactances  in 
potential  transformer  tests. 

If  co2(72V22  is  negligible  compared  to  unity, 
Z2  =  7J2  +  j«  [L2  -  C2r22j. 

That  is,  the  circuit  acts  as  if  it  had  a  resistance  R2  and  an  induc- 
tance (Z/2  —  C2r22).  The  resistance  r2  may  be  varied  by  the 
slider.  The  inductance  L2  may  have  a  fixed  value;  if  so,  it  can 
be  placed  at  a  distance  from  the  vibration  galvanometer  and 
other  apparatus,  thus  avoiding  trouble  from  stray  fields. 

The  vector  solution  for  the  ratio  and  phase  angle,  when  the 
connections  shown  in  Fig.  363  are  used,  is  obtained  as  follows. 

Referring  to  Fig.  365,  the  direction  and  magnitude  of  the  line 
ab  which  represents  the  drop  across  Z2  may  be  controlled  by 
adjusting  R2  and  L2,  and  the  point  6  may  be  made  to  coincide 


588  ELECTRICAL  MEASUREMENTS 

with  c.     When  this  has  been  done,  that  is,  at  balance,  if  L2  is  the 
effective  inductance  of  Z2, 

and 


i  =  V^TE 


)2  +  co2L22 


Id}  Lo 


FIG.  365.— Vector  diagram  for  Fig.  363. 

To  obtain  the  phase  angle, 

y  =  a  —  8. 

At  balance,  tan  a  =  -^—  and  tan  8  =  p     f   p  • 

Vz  leads  V\  by 

Z/2£o  LZ& 

tan"1 — — —^-^ — —  =  tan"1   ^  ,„    w  1  ; 


Comparison  Tests  of  Instrument  Transformers.11 — Current 
and  potential  transformers  .may  be  compared  with  standard 
transformers  of  the  same  rating  whose  constants  are  known,  by  a 
method  developed  by  Agnew. 

When  dealing  with  current  transformers  the  two  primaries  are 
connected  in  series,  while  the  two  secondaries  are  connected  to  the 
current  coils  of  two  induction  watt-hour  meters  whose  potential 
coils  are  excited  from  a  common  source.  The  phase  difference 
between  the  P.D.  applied  to  the  meters  and  the  current  in  the 
primaries  of  the  transformers  should  be  adjustable.  Fig.  366 
shows  the  connections  for  testing  both  current  and  potential  trans- 
formers by  this  method.  If  the  applied  voltage  and  current  were 
in  phase  and  the  meters  were  perfectly  accurate,  the  relative  value 


INSTRUMENT  TRANSFORMERS 


589 


of  the  transformer  ratios  would  be  found  by  taking  the  ratio  of  the 
numbers  of  revolutions  made  by  the  two  watt-hour  meters  in  the 
same  time.  If  the  power  factor  were  other  than  unity,  the  ratio 
of  the  revolutions  would  be  affected  by  an  amount  dependent  on 
the  difference  in  the  phase  angles  of  the  transformers. 


Voltage 
Supply 


Arrangement  for  Testing  Current  Transformers 


(JOOOOj 

,  Q                m                                     f^  J 

r  00000  ^ 

Trans.  1 

Al 

A2 

Trans.2 

B\ 

*~l   °  
1  /»2 

UtOP-OJ 

t        ° 

LftMJU 

00                 00 

Aux.Gurrent  Supply      Meter  ^1                  Meter  .8            (t)  (£)  (r? 

Arrangement  for  Testing  Voltage  Transformers 

FIG.  366. — Connections  for  Agnew  method  of  comparing  instrument  trans- 
formers by  use  of  watt-hour  meters. 

To  eliminate  differences  in  the  calibration  of  the  meters  two 
runs  are  made,  the  meters  being  interchanged. 

Let  6  =  power  factor  angle  or  the  phase  difference  of  the  current  (or 

voltage)   in  the  primary  of  the   transformer  and  the 

auxiliary  voltage  (or  current)  applied  to  the  watt-hour 

meter.     6  is  taken  +  for  lagging  current. 

niA  and  ra#  =  the  rates  of  meters  A  and  B  respectively,  that  is,  the 

Watt-hours  registered 
values  of  the  raho  ~ f  me  watt-hours" 

Kh  =  watt-hour  constant  of  the  meters  as  marked  on  the  discs. 


590  ELECTRICAL  MEASUREMENTS 

(NA)I  and  (NA)Z  =  number  of  revolutions  made  by  meter  A  when  connected 

to  transformers  1  and  2,  respectively. 
(Ns)i  and  (Ns}?  =  number  of  revolutions  made  by  meter  B  when  connected 

to  transformers  1  and  2,  respectively. 

/3i  and  02  =  phase  angles  of  the  transformers  1  and  2,  respectively, 
taken  +  when  the  current  or  voltage  in  the  secondary 
lags  the  primary  current  or  voltage  reversed. 
Ri  and  R2  =  ratios  of  the  transformers  1  and  2. 

Suppose  that  meter  A  is  connected  to  transformer  No.  1,  and 
that  the  phase  of  the  auxiliary  voltage  is  adjusted  so  that  0  is 
large.  The  watt-hours  registered  on  the  meter  dials  are  given 
by  (Kh)  (NA)  which,  when  corrected  for  the  rate  of  the  meter,  is 

(Kh)(N A)  (  —  -'}'    As  the  meter  is  operated  through  a  trans- 
\mA/ 

former  of  ratio   Ri.,  this  quantity  must  be  multiplied  by  Ri. 
giving  (Kh)(NA)i(Ri) To  obtain  the  true  watt  hours  by 

cos  0  cos  0 

meter  A  this  result  must  be  multiplied  by-  — -^  =  -     //>.  Q\' 

cos  u        cos  \u  ~T~  P) 

(see  page  577).     Therefore  from  meter  A, 

1        cos  0 

corrected  watt-hours  =  (Kt)(NA)i(Mij~        ~~77r~i~^v 

mA  cos   (0  +  Pi) 

Similarly  for  the  meter  B  connected  to  transformer  2, 

x  1        cos  0 


corrected  watt-hours  =  (jK" 


'"mB  cos  (0  + 

L»\Jo    C7  /  -*  f    \     /  -g-^   \    JL  CvJo    C 


••  cos  (tf  +  p.) 

and  when  the  meters  are  interchanged, 

l  CQS  ^  1  cos 


If  .the  test  is  made  at  unity  power  factor,  0  =  0,  and  since  0  is  a 

small  angle, 

(la) 
(2a) 


=J 


To  determine  the  difference  of  the  phase  angles  of  the  trans- 
formers, a  test  is  made  at  low  power  factor. 


INSTRUMENT  TRANSFORMERS  591 


Using  the  relation 
cos  0 


cos    (0  +  /3)       cos  j3  (1  -  tan  0  tan  /3) 

and  remembering  that  ft  is  a  small  angle  whose  cosine  is  very 
nearly  unity,  1  and  2  give 

(NA)2(NB)^  /R*\  2  =  1  -  2  tan  0  tan  02  = 
(NA)I(NB)I  \Rj      ~  1  -  2  tan  (9  tan  ft  ~ 

1+2  tan  0  (tan  ft  —  tan  ft)  approximately. 


Rotary  standard  watt-hour  meters  are  convenient  for  making  the 
tests,  for  the  revolutions  may  be  accurately  read  from  the  dials. 

References 

1.  "Electrical  Measurements  on  Circuits  Requiring  Current  and  Potential 
Transformers,"  L.  T.  ROBINSON,  Trans.  American  Institute  Electrical  Engi- 
neers, vol.  28,  1909,  p.  1005. 

2.  "The  Testing  of  Instrument  Transformers,"  P.  G.  AGNEW  and  F.  B. 
SILSBEE,  Trans.  American  Institute  Electrical  Engineers,  vol.  31,  1912,  p. 
1635. 

3.  "Potential  Transformer  Testing,"  J.  R.  CRAIGHEAD,  Trans.  American 
Institute  Electrical  Engineers,  vol.  31,  1912,  p.  1627. 

4.  "The  Phase  Angle  of  Current  Transformers,"  CHESTER  L.  DAWES, 
Trans.  American  Institute  Electrical  Engineers,  vol.  34,  1915,  p.  1585. 

5.  "The  Calibration  of  Current  Transformers  by  Means  of  Mutual  Induc- 
tances," CHARLES  FORTESCUE,  Trans.  American  Institute  Electrical  Engi- 
neers, vol.  34,  1915,  p.  1599. 

6.  "The  Determination  of  the  Constants  of  Instrument  Transformers," 
P.  G.  AGNEW  and  T.  T.  FITCH,  Bulletin  Bureau  of  Standards,  vol.  6,  1909, 
p.  281,  Scientific  Paper  No.  130. 

7.  "The  Determination  of  the  Ratio  of  Transformation  and  of  the  Phase 
Relations  in  Transformers,"  E.  B.  ROSA  and  M.  G.  LLOYD,  Bulletin  Bureau  of 
Standards,  vol.  6,  1909,  p.  1. 

8.  "On  the  Use  of  Mutual  Inductometers,"  A.  CAMPBELL,  Proc.  Physical 
Society  of  London,  vol.  22,  1910,  p.  207. 

9.  "Determination  of  the  Constants  of  Instrument  Transformers,"  F.  A. 
LAWS,  Electrical  World,  vol.  55,  1910,  p.  223. 

10.  "Some  Recent  Developments  in  Exact  Alternating-current  Measure- 
ments,". C.  H.  SHARP  and  W.  W.  CRAWFORD,  Trans.  American  Institute 
Electrical  Engineers,  vol.  29,  1910,  p.  1517. 

11.  "A  Watt-hour  Meter  Method  of  Testing  Instrument  Transformers," 


592  ELECTRICAL  MEASUREMENTS 

P.  G.  AGNEW,  Bulletin  Bureau  of  Standards,  vol.  11,  1915,  p.  347,  Scientific 
Paper  No.  233. 

12.  "Accuracy  of  the  Formulas  for  the  Ratio,  Regulation,  and  Phase 
Angle  of  Transformers,"  P.  G.  AGNEW  and  F.  B.  SILSBEE,  Bulletin  Bureau 
of  Standards,  vol.  10,  1914,  p.  27$,  Scientific  Paper  No.  211. 

13.  "A  Study  of  the  Current  Transformer  with  Particular  Reference  to 
Iron  Loss,"  P.  G.  AGNEW,  Bulletin  Bureau  of  Standards,  vol.  7,  1911,  p. 
423,  Scientific  Paper  No.  164. 

14.  "Current-ratio  and  Phase-angle  Test  of  Series  Transformer,"  H.  S. 
BAKER,  Electrical  World,  vol.  57,  1911,  p.  234. 

15.  "Theory  and  Design  of  the  Current  Transformer,"  A.  P.  YOUNG, 
Journal  Institution  of  Electrical  Engineers,  vol.  45,  1910,  p.  670. 

16.  "Notes    on    Instrument    Transformers,"    K.    EDGCUMBE,    Electrical 
Review  (London),  vol.  67,  1910,  p.  163. 

17.  "Some  Measurements  on  Phase  Displacements  in  Resistances  and 
Transformers,"  C.  V.  DRYSDALE,  Electrician,  vol.  57,  1906,  pp.  726,  783. 

18.  "Operation  of  the  Series  Transformer,"  EDWARD  L.  WILDER,  Electric 
Journal,  vol.  1,  1904,  p.  451. 

19.  "The  Series  Transformer,"  E.  S.  HARRAR,  Electrical  World,  vol.  51, 
1908,  p.  1044. 

20.  "A  Milliampere  Current  Transformer,"  EDWARD  BENNETT,  Trans. 
American  Institute  Electrical  Engineers,  vol.  33,  1914,  p.  571. 

21.  "tiber    einen    Spannungsteiler    fur    Hochspannungsmessungen,"   E. 
ORLICH  AND  H.  SCHULTZE,  Archiv.  fvr  Elektrotechnik,  vol.  1,  1912,  p.  1. 


CHAPTER  XIII 
THE  CALIBRATION  OF  INSTRUMENTS 

This  chapter  deals  chiefly  with  indicating  electrical  instruments 
intended  for  use  in  engineering  work. 

Accuracy  and  Precision. — Every  experimenter  must  form  his 
own  estimate  of  the  accuracy,  or  approach  to  the  absolute  truth, 
obtained  by  the  use  of  his  instruments  and  processes  of  measure- 
ment. He  must  remember  that  a  high  precision,  or  agreement  of 
the  results  among  themselves,  is  no  indication  that  the  quantity 
under  measurement  has  been  accurately  determined.  For 
instance,  under  favorable  conditions  one  may  be  certain  of  the 
reading  of  a  voltmeter  (at  about  100  volts)  to  J^Q  of  1  Per  cent. 
At  the  same  time  the  instrument  may  be  several  per  cent,  in 
error,  and  the  true  value  of  the  measured  P.D.  will  remain 
unknown  until  the  instrument  has  been  calibrated. 

Generally  speaking,  in  any  piece  of  experimental  work  one 
should  aim  at  as  high  a  degree  of  accuracy  in  the  final  result  as 
can  be  attained  without  undue  labor  and  expense.  This  conduces 
to  discipline  among  the  observers,  as  it  discourages  slipshod 
methods  of  observation.  It  also  aids  in  the  collection  of 
reliable  engineering  data  for  use  on  other  occasions.  But  it  is 
to  be  remembered  that  the  expense  and  the  labor  increase  very 
rapidly  as  the  required  degree  of  accuracy  is  raised.  Conse- 
quently the  determination  of  what  the  required  degree  of  ac- 
curacy shall  be,  becomes  an  economic  problem. 

Clear  ideas  concerning  the  distinction  between  accuracy  and 
precision  are  especially  important  to  those  beginning  experimental 
work. 

During  the  progress  of  many  tests  the  obvious  thing,  and  there- 
fore the  factor  on  which  the  beginner's  attention  is  likely  to  be 
fixed,  is  the  uncertainty  in  determining  the  best  representative 
values  of  the  readings  of  his  instruments,  for  frequently  the  cir- 
cuit conditions  are  fluctuating  so  that  close  attention  in  reading 
38  593 


594  ELECTRICAL  MEASUREMENTS 

and  the  averaging  of  many  observations  are  necessary.  After 
the  experimental  work  has  begun  these  things  may  distract  the 
beginner's  attention  from  insidious  constant  errors  and  errors  of 
method  so  that  these  are  scarcely  thought  of  though  they  may 
be  of  vastly  greater  importance  than  the  errors  of  reading.  For 
this  reason  it  is  necessary  to  study  carefully  any  proposed  test 
or  method  of  measurement  in  order  that,  as  far  as  possible,  all 
constant  errors  and  errors  of  method  may  be  eliminated  before 
the  experimental  work  is  begun. 

Another  result  of  this  preliminary  study  should  be  a  proper 
division  of  the  labor  among  the  various  component  measurements. 
Generally  there  are  some  measurements  whose  effects  on  the 
final  result  are  small,  and  therefore  labor  expended  in  making 
numerous  readings  is  wasted.  This,  however,  does  not  imply  that 
when  they  are  taken,  the  readings  giving  these  less  important 
components  may  be  made  in  a  slovenly  manner. 

In  an  investigation,  the  preliminary  study  is  frequently  a  very 
difficult  part  of  the  work,  involving  as  it  does  a  careful  analysis 
of  the  workings  of  the  apparatus,  a  wide  range  of  theoretical 
knowledge  and  an  accurate  understanding  of  the  behavior  and 
sources  of  error  in  many  different  kinds  of  instruments. 

In  a  complicated  experimental  investigation,  to  complete  the 
elimination  of  constant  errors  and  errors  of  method,  a  second 
determination  of  the  quantity  under  measurement  should,  if 
possible,  be  made  by  an  independent  method,  using  other  apparatus. 

The  beginner  must  keep  in  mind  that  it  is  scarcely  possible  to 
measure  any  of  the  electrical  magnitudes  as  he  finds  them  in 
engineering  practice,  without  changing  the  conditions  of  the 
circuit  in  which  the  measurement  is  made  and  thus  altering  the 
very  thing  which  is  to  be  determined.  An  ammeter  when  intro- 
duced into  a  circuit  alters  the  current,  and  an  electromagnetic 
voltmeter  alters  the  potential  difference  to  which  it  is  applied. 
In  the  vast  majority  of  cases,  these  effects  are  negligible,  but  the 
possibilities  of  error  due  to  the  alterations  of  circuit  conditions 
must  not  be  lost  sight  of. 

Calibration  Before  and  After  Tests. — In  making  careful  accep- 
tance tests  of  electrical  machinery,  the  indicating  instruments 
should  be  calibrated  before  the  test  and  a  check  calibration  made 
at  the  conclusion  of  the  work.  This  allows  the  various  runs  to 


THE  CALIBRATION  OF  INSTRUMENTS         595 

be  worked  up  while  the  test  is  in  progress,  which  is  highly  desir- 
able, as  it  insures  that  all  necessary  data  are  being  taken  and  that 
the  procedure  of  the  observers  is  correct.  The  check  calibra- 
tion eliminates  questions  as  to  the  accuracy  of  the  instruments 
and  as  to  whether  or  not  they  have  been  tampered  with  or 
injured  in  any  way. 

Choice  of  Instruments. — In  selecting  the  instruments  for  a 
particular  piece  of  work  those  should  be  chosen  which  will  give 
good  deflections;  that  is,  deflections  in  a  favorable  part  of  the 
scale,  and  of  such  a  magnitude  that  the  required  precision  of 
reading  is  readily  attained.  The  choice,  therefore,  involves  a 
preliminary  study  of  the  conditions  of  the  test  in  order  to 
determine  approximately  the  magnitudes  of  the  quantities 
involved.  It  must  then  be  decided  whether  or  not  the  desired, 
and  obtainable,  degree  of  accuracy  in  the  final  result  is  such  that 
careful  calibrations  are  necessary. 

Often  one  knows  from  previous  experience  that  his  instru- 
ments are  correct  to  within  1  or  2  per  cent,  and  instances  are 
continually  arising  where  the  conditions  are  such  that  an  accu- 
racy of  2  or  3  per  cent  is  sufficient.  In  such  cases,  where 
differences  of  nearly  equal  quantities  are  not  involved,  there  is 
no  point  in  calibrating  the  instruments  to  0.2  per  cent,  for 
example.  Again,  there  are  many  cases  where  the  magnitudes 
to  be  determined  cannot  be  estimated  a  priori,  and  a  certain 
amount  of  rough  preliminary  work  is  necessary  to  determine 
the  most  advantageous  ranges  of  the  instruments.  In  such  a  case 
the  calibrations  should  be  deferred  until  the  proper  instruments 
have  been  selected. 

Attention  to  these  simple  matters  may  save  the  beginner  much 
valuable  time,  and  may  possibly  prevent  his  arriving  on  the 
ground  for  a  test  without  the  proper  equipment. 

Sources  of  Error  in  Instruments 

The  various  sources  of  error  which  have  been  referred  to  in 
discussing  particular  instruments  will  be  recapitulated. 

Errors  of  Reading. — In  general,  the  construction  of  the  pointer 
and  the  graduation  of  the  scale  should  be  such  that  under  steady 
conditions  the  position  of  the  pointer  may  be  read,  by  estima- 
tion, to  one-tenth  of  a  scale  division.  This  is  readily  attained 


596  ELECTRICAL  MEASUREMENTS 

in  direct-current  instruments  of  the  moving-coil  type  and  in 
wattmeters  over  the  larger  part  of  the  scale.  Alternating- 
current  ammeters  and  voltmeters  have  scales  on  which  the 
graduations  are  crowded  together  at  the  lower  end  and  possibly 
the  upper  end  also,  so  this  precision  of  reading  may  be  ob- 
tained between  25  per  cent  and  about  90  per  cent  of  the  full- 
scale  reading. 

Under  commercial  conditions,  one  must  expect  irregular  fluc- 
tuations in  the  readings.  If  the  fluctuations  are  not  too  great, 
the  readings  may  be  averaged  mentally,  but  it  is  generally  best 
to  record  a  series  of  readings  taken  at  regular  intervals  and 
calculate  the  average.  In  industrial  testing,  it  is  surprising  how 
closely  the  averages  from  various  runs  made  under  the  same 
general  conditions  will  check  one  another,  even  though  there  are 
great  momentary  fluctuations. 

In  selecting  instruments  for  industrial  testing,  attention  must 
be  given  to  the  damping  (often  very  defective  in  alternating- 
current  instruments),  otherwise  the  swinging  of  the  pointer  in 
its  own  natural  period  will  be  superposed  on  the  deflection  due 
to  the  load,  and  will  render  it  quite  impossible  to  obtain  the  true 
reading.  If  several  instruments  have  to  be  read  simultaneously, 
their  times  of  vibration  and  damping  should  be  such  that  they 
will  keep  step  as  the  load  varies. 

MECHANICAL  ERRORS 

Friction. — The  effects  of  friction  at  the  jewels  and  pivots  should 
be  reduced  to  a  minimum.  This  means  that  the  construction 
must  be  of  the  best  and  that  the  ratio  of  torque  to  total  weight 
of  the  moving  parts  must  be  high.  Various  writers  assign  values 
ranging  from  J-^o  to  %  for  the  ratio, 

Torque  in  gram-centimeters,  at  full-scale  deflection 
Weight  of  moving  element  in  grams 

Before  taking  any  instrument  from  the  laboratory  for  use  on 
a  test,  one  should  satisfy  himself  as  to  the  pivot  friction  and  free- 
dom of  motion  of  its  movable  element  by  putting  it  in  circuit 
and  slowly  carrying  the  reading  over  the  whole  scale,  stopping 
at  several  points.  If  there  is  undue  friction,  it  will  be  made 


THE  CALIBRATION  OF  INSTRUMENTS         597 

evident  by  a  sudden  change  of  reading  when  the  instrument  is 
tapped.  Excessive  friction  may  be  due  to  a  cracked  jewel,  or 
to  other  injury,  due  to  dropping  the  instrument.  Again,  the 
freedom  of  motion  of  the  movable  system  may  be  impeded  by 
the  buckling  of  the  paper  scale,  due  to  dampness,  or  to  projecting 
fibers  of  the  paper,  which  cause  the  pointer  to  stick.  Air 
dampers,  which  have  very  small  clearances  may  also  give 
trouble  by  getting  out  of  adjustment  and  lightly  dragging  on  the 
damping  box.  In  direct-current  moving-coil  instruments,  trouble 
may  be  due  to  dust — possibly  magnetic,  in  which  case  it  is  hard 
to  dislodge — in  the  air  gap. 

Springs. — The  assumption  that  the  deflections  of  all  sorts  of 
instrument  springs  are  always  proportional  to  the  deflecting 
moment  is  not  tenable.  The  exact  fulfilment  of  Hooke's  law  de- 
pends on  the  shape  of  the  spring  and  on  the  method  of  mounting. 
In  deflectional  instruments  the  peculiarities  of  the  springs  are 
taken  care  of  in  the  initial  calibration  and  introduce  no  trouble 
unless  the  spring  is  subsequently  deformed  in  some  manner; 
but  when  an  equally  divided  scale  and  a  torsion  head  are  used, 
as  in  the  Siemen's  dynamometer,  the  instrument  must  be  tested 
at  several  points  and  a  calibration  curve  drawn. 

Zero  Shift. — This  is  due  to  a  gradual  yielding  of  the  spring  when 
the  instrument  is  kept  at  a  large  deflection  for  a  considerable 
time,  an  hour  or  several  hours.  On  breaking  the  circuit  the 
pointer  does  not  return  at  once  to  its  original  zero  position,  but 
will  gradually  assume  it. 

The  magnitude  of  the  zero  shift  depends  on  the  design  and 
material  of  the  spring  and  on  the  nearness  with  which  the  elastic 
limit  is  approached.  Springs  which  are  used  in  high-resistance 
circuits,  such  as  those,  of  voltmeters  and  wattmeters,  may  be 
made  of  a  material  having  good  elastic  properties,  such  as  a 
bronze,  for  no  limit  is  set  as  to  spring  resistance.  Low-resistance 
springs,  for  millivoltmeters,  have  a  high  percentage  of  copper  and 
show  a  larger  zero  shift  than  the  bronze  springs. 

Temperature  Coefficients  of  Springs. — With  a  rise  of  tempera- 
ture, the  elasticity  of  the  springs  decreases  about  0.03  or  0.04 
per  cent  per  degree  C.  This,  if  uncompensated,  would  cause 
an  increase  of  like  amount  in  the  deflection.  In  many  cases 
electrical  and  magnetic  changes  afford  a  partial  compensation. 


598  ELECTRICAL  MEASUREMENTS 

Balancing. — Accurate  balancing  of  the  movable  system  is 
essential,  for  commercial  instruments  should  not  require  careful 
levelling.  As  a  test  the  instrument  should  be  tilted  from  its 
normal  position  in  various  directions  and  the  pointer  observed. 
If  lack  of  balance  is  found  to  be  present  and  the  instrument  must 
be  used,  it  should  be  set  up,  using  a  level,  the  same  precaution 
being  taken  during  the  calibration.  The  rebalancing  should  be 
done  by  an  experienced  person. 

Scale  Errors. — The  cardinal  points  on  the  scale  are  supposed 
to  be  laid  off,  for  each  particular  instrument,  by  comparison  with 
a  standard.  However,  the  subdivisions  are  frequently  very 
carelessly  made  and  their  irregularities  are  often  apparent  on 
inspection.  The  calibration  curves  for  such  irregular  scales  are 
" lumpy"  and  the  calibration  points  must  be  taken  near  together. 

Corrosion. — Hard-rubber  covers  and  instrument  bases  which 
are  imperfectly  vulcanized  may  give  trouble.  The  free  sulphur 
attacks  delicate  wires,  controlling  springs,  and  suspensions, 
causing  gradual  deterioration  and  finally  total  failure.  The 
effect  on  the  indications  of  the  instrument  is,  of  course,  pro- 
gressive. Fine  wires  insulated  with  soft-rubber  tubes,  as  is 
common  for  internal  connections,  may  suffer  in  the  same  way. 

ELECTRICAL  AND  MAGNETIC  ERRORS 

Shunts. — Care  must  be  taken  that  shunts  suffer  no  mechanical 
injury.  In  making  connections  for  a  test  they  should  be  firmly 
bolted  into  the  circuit,  all  contacts  being  clean.  Imperfect 
contact  at  one  end  of  the  shunt  may  result  in  unequal  heating 
and  a  consequent  thermo-electromotive-force  error;  but  the  over- 
zealous  application  of  the  monkey  wrench  should  be  avoided,  for 
if  the  shunt  is  not  properly  supported  some  of  the  soldered  joints 
where  the  resistance  strips  are  sweated  into  the  terminal  blocks 
may  be  broken,  and  though  no  damage  is  visible  the  shunt  may 
be  rendered  entirely  untrustworthy  and  the  test  useless.  The 
current  leads  should  be  of  ample  size,  so  as  to  assist  rather  than 
to  hinder  the  dissipation  of  the  heat  from  the  shunt.  During 
calibrations,  especially  where  high-capacity  shunts  are  involved, 
current  connections  identical  with  those  of  regular  service  must 
be  used,  so  that  the  current  may  be  properly  distributed  before 
the  potential  terminals  are  reached. 


THE  CALIBRATION  OF  INSTRUMENTS         599 

Millivoltmeter  Leads. — External  shunt  ammeters  must  be 
calibrated  with  the  same  set  of  leads  connecting  the  shunt  and 
the  millivoltmeter  that  is  to  be  used  in  the  subsequent  test. 
Frequently  special  leads  30  or  40  feet  long  must  be  used  in  order 
to  remove  the  millivoltmeter  from  stray  fields,  or  to  allow  it 
to  be  placed  where  it  can  be  easily  read.  Such  leads  should  be 
of  large  diameter  to  reduce  the  resistance,  and  should  be  provided 
with  proper  terminals. 

In  all  cases  when  connecting  the  millivoltmeter  and  the  shunt, 
care  must  be  taken  that  all  contacts  are  clean  and  firmly  set  up. 
The  leads  should  be  carefully  examined  to  see  that  they  are  not 
broken  inside  the  insulation  or  where  they  are  soldered  to  the 
terminals. 

Thermo -electromotive  Forces. — The  material  of  the  resistance 
strips  used  in  shunts  should  have  a  small  thermo-electromotive 
force  when  opposed  to  copper.  Manganin  is  the  best.  The 
existence  of  a  thermo-electromotive  force  may  be  demonstrated 
by  sending  full  current  through  the  shunted  instrument  for  a 
considerable  time  and  then  breaking  the  main  circuit.  The 
millivoltmeter  will  not  return  at  once  to  zero.  This  effect  may 
be  differentiated  from  the  zero-set  by  breaking  the  milli volt- 
meter circuit.  Switch-board  shunts  are  likely  to  be  defective 
in  this  respect,  and  should  not  be  used  in  very  careful  work  until 
they  have  been  investigated. 

Effect  of  External  Temperatures. — Variations  of  room  tem- 
perature produce  only  small  errors  in  soft-iron  ammeters  with  a 
spring  control,  for  as  the  spring  weakens,  the  permeability  of  the 
iron  decreases  in  such  an  amount  as  practically  to  compensate  for 
it.  In  the  voltmeter  there  is  an  additional  source  of  error  in  the 
alteration  of  the  resistance.  The  windings  will  be  of  copper  and 
the  series  resistance  of  a  material  with  a  zero  temperature  coef- 
ficient. The  net  effect  will  depend  on  their  relative  magnitude; 
it  will  be  small  in  high-range  instruments. 

The  only  effect  on  current  dynamometers,  with  the  coils  in 
series,  is  to  alter  the  spring,  0.03  or  0.04  per  cent  per  degree  C., 
causing  the  instrument  to  read  too  high.  The  effect  on  dyna- 
mometer voltmeters  is  on  the  resistance  as  well  as  on  the  spring. 

With  a  rise  of  temperature,  the  magnets  of  a  moving-coil 
voltmeter  decrease  in  strength,  the  springs  weaken,  and  the 


600  ELECTRICAL  MEASUREMENTS 

total  resistance  increases  somewhat.  In  a  150-volt  instrument 
the  net  effect  is  negligible,  but  lower-range  instruments,  made 
by  using  the  same  galvanometer  element  and  a  smaller  series 
resistance,  will  be  affected  by  an  amount  increasing  with  the 
diminution  of  the  range,  0.4  per  cent  per  degree  being  the  extreme 
value,  for  then  the  copper  of  the  moving  coil  becomes  relatively 
more  important.  Therefore,  in  accurate  work  very  low-range 
instruments  should  be  used  with  care.  Frequently,  in  laboratory 
voltmeters,  a  thermometer  is  inserted  in  the  case  as  an  aid  in 
making  the  temperature  corrections. 

From  the  standpoint  of  external  temperature  effects  the  shunt 
and  the  millivoltmeter  in  shunted  ammeters  should  be  of  the  same 
material,  so  that  they  may  have  practically  the  same  tempera- 
ture coefficient.  As  the  shunt  is  best  made  of  manganin,  this 
implies  that  a  resistance  also  of  .manganin  be  used  in  series  with 
the  copper  moving  coil,  so  as  to  obtain  an  approximation  to  the 
ideal  condition.  This  means  that  the  drop  in  precision  ammeters 
is  considerable — 150  to  200  millivolts  at  full  load.  The  drop 
in  switchboard  shunts  is  about  50  millivolts. 

Internal  Heating  Errors. — In  shunted  ammeters,  errors  may 
arise  from  the  unequal  percentage  increase  of  the  resistances  of 
the  shunt  and  the  millivoltmeter  parts,  due  to  the  passage  of  the 
current.  In  old  instruments,  with  internal  copper  shunts,  this 
error  is  very  pronounced.  For  instance,  in  a  certain  150-ampere 
instrument,  it  was  found  to  be  4  per  cent  at  full-scale  deflection. 
In  modern  high-resistance  precision  ammeters,  this  error  ceases 
to  be  troublesome. 

In  voltmeters,  if  they  are  kept  in  circuit,  there  will  be  heating 
of  the  series  resistance  and  movable  coil  due  to  the  passage  of  the 
current,  but  on  account  of  the  low  net  temperature  coefficient, 
the  resulting  error  will  not  be  great.  High  resistance  mul- 
tipliers should  be  properly  ventilated. 

In  direct-current  instruments  (150-volt)  the  expenditure  of 
energy  is  small,  about  1.5  watts  at  full-scale  deflection.  In 
wattmeters  and  alternating-current  voltmeters,  together  with 
their  accompanying  multipliers,  much  more  heat  must  be  dissi- 
pated on  account  of  the  lower  resistances,  about  7  watts  in  a 
150-volt  instrument  at  full-scale  deflection.  In  any  case  the 
construction  should  be  such  that  the  heat  is  kept  away  from  the 


THE  CALIBRATION  OF  INSTRUMENTS         601 

springs  and  the  copper  movable  coil.  Both  instruments  and 
multipliers  should  be  properly  ventilated. 

Stray  Fields. — One  of  the  most  troublesome  sources  of  error 
in  industrial  testing  is  due  to  the  stray  fields  from  busbars, 
feeders,  motors,  masses  of  iron,  etc.  These  may  so  modify  the 
strength  of  the  field  in  which  the  movable  coil  swings  that  the 
indications  of  the  instrument  are  entirely  untrustworthy. 
Especial  care  must  be  exercised  when  working  near  switchboards. 

Stray  fields  due  to  ordinary  working  conditions  are  not  likely 
to  produce  permanent  alterations  in  the  instruments,  but  vio- 
lent short-circuits  may  cause  permanent  changes  in  the  strength 
of  the  magnets  and  occasion  very  large  errors.  This  is  especially 
true  of  direct-current  watt-hour  meters.  In  this  case  the  stray 
field  is  that  due  to  the  current  coils.  Fig.  266  shows  the  normal 
distribution  of  magnetism  in  the  drag  magnets  as  well  as  the 
distribution  after  a  short-circuit.  Strong  alternating  stray  fields, 
due  to  short-circuits,  may  also  greatly  modify  the  strength  of  any 
permanent  magnets  in  their  neighborhood.  If  such  an  accident 
has  happened  with  either  alternating  or  direct  currents,  no  reli- 
ance should  be  placed  on  the  instruments  until  they  have  been 
tested  and  found  to  be  correct. 

Direct-current  stray  fields  of  ordinary  strength  cause  a  per- 
centage change  throughout  the  scale  in  the  indications  of  moving- 
coil  ammeters  and  voltmeters.  Of  course,  they  produce  no  effect 
on  alternating-current  instruments.  Alternating  stray  fields  of 
ordinary  strength  have  no  effect  on  direct-current  moving-coil 
voltmeters  and  ammeters,  but  will  affect  ammeters,  voltmeters, 
and  wattmeters  in  which  the  current  is  of  the  same  frequency 
as  the  field. 

The  effect  on  dynamometer  instruments  will  depend  on  the 
angular  position  of  the  movable  coil  with  respect  to  the  direction 
of  the  stray  field,  being  a  maximum  when  the  plane  of  the  coil  is 
in  the  direction  of  the  field  and  zero  when  it  is  perpendicular 
to  it.  Assuming  that  the  stray  field  is  fixed  in  direction,  dyna- 
mometer instruments  with  torsion  heads  should  be  set  up  in 
such  a  position  that  the  movable  coil  is  perpendicular  to  the  field. 
The  proper  position  is  found  by  sending  full  current  through 
the  movable  coil  alone  and  turning  the  entire  instrument  in 
azimuth  until  the  deflection  disappears. 


602  ELECTRICAL  MEASUREMENTS 

To  detect  the  presence  of  a  stray  field,  the  instrument  should 
be  read  and  then  immediately  turned  through  180°  and  read 
again,  the  circuit  conditions  being  maintained  as  constant  as 
possible.  If  no  stray  field  is  present,  the  readings  will  check. 
If  a  wattmeter  is  being  used,  current  may  be  sent  through  the 
potential  circuit  alone  and  the  instrument  slowly  turned  in 
azimuth.  Any  deflection  observed  will  be  due  to  the  stray  field. 

The  stray  fields  due  to  heavy  currents  in  the  leads  to  the  in- 
struments themselves  must  not  be  neglected.  The  leads  must  be 
free  from  loops  and  coils,  should  run  straight  away  and  should  be 
twisted.  Especial  care  must  be  exercised  when  testing  direct- 
current  watt-hour  meters  in  situ,  that  the  stray  fields  from  the  tem- 
porary connections,  such  as  the  necessary  jumpers,  do  not 
vitiate  the  results,  especially  at  light  loads.  Do  not  set  moving- 
coil  instruments  on  sheets  of  "tin,"  which  are  tinned  iron,  and 
do  not  place  instruments  too  near  together.  As  the  field  strength 
in  alternating-current  instruments  is  small,  they  are  more  sus- 
ceptible to  these  errors  than  direct-current  instruments  of  the 
moving-coil  type.  In  general,  one  cannot  assume  that  stray 
fields  are  constant  in  either  magnitude  or  direction. 

Careful  attention  must  be  given  to  these  points  when  deciding 
on  the  location  and  arrangement  of  apparatus  for  a  test;  for  in 
any  case  where  results  are  called  in  question,  unless  one  can  prove 
that  there  were  no  stray-field  errors,  the  measurements  have  no 
standing.  Shielded  instruments  obviate  these  troubles. 

Electrostatic  Attraction. — Electrostatic  attraction  between  the 
fixed  and  movable  members  may  cause  erroneous  deflections; 
for  instance,  in  wattmeters  which  are  operated  from  instrument 
transformers.  In  this  case  the  remedy  is  to  connect  the  current 
and  potential  circuits  by  a  bit  of  the  finest  fuse  wire.  Again, 
glass  and  hard-rubber  covers  sometimes  give  trouble.  They 
should  not  be  rubbed  immediately  before  a  reading  is  taken. 
The  surface  charges  may  be  dissipated  by  breathing  on  the 
instrument.  High  range  instruments  having  metal  covers  which 
are  supported  by  insulating  bases  are  likely  to  give  trouble. 
The  secondary  circuits  of  instrument  transformers  should  be 
grounded. 

Eddy  Currents. — Eddy  currents  induced  in  massive  coils,  in 
metal  frames  supporting  the  coils  or  in  metal  covers,  may  be  a 


THE  CALIBRATION  OF  INSTRUMENTS         603 

source  of  error  in  alternating-current  work.  These  effects  may 
be  pronounced  in  wattmeters  when  working  at  low  power  fac- 
tors; of  course  they  are  absent  when  direct  currents  are  used. 

Current  Distribution. — Distribution  errors  may  be  met  with 
in  alternating-current  instruments  with  massive  coils,  the  cur- 
rent not  distributing  itself  uniformly  over  the  cross-section  of  the 
conductor  as  it  does  when  direct  current  is  used.  This  also 
may  cause  the  alternating-  and  direct-current  calibrations  to 
differ. 

Frequency  and  Wave  Form. — There  is  a  possibility  of  error 
in  dynamometer  voltmeters  and  wattmeters  and  in  soft-iron 
voltmeters,  due  to  frequency,  if  the  reactance  of  the  instrument 
becomes  unduly  high  in  proportion  to  the  resistance.  Espe- 
cially should  one  be  on  his  guard  in  investigation  work  where 
abnormal  frequencies  are  sometimes  employed.  An  instrument 
which  is  commercially  correct  at  60  cycles  may  be  much  in  error 
at  500  cycles.  Eddy-current  effects  are  much  accentuated  at 
high  frequencies. 

Soft-iron  instruments  may  be  subject  to  wave-form  errors 
arising  from  saturation  effects,  but  with  good  modern  instruments 
no  trouble  is  likely  to  be  experienced. 

Induction  instruments  have  errors  all  their  own,  due  to  the 
fact  that  when  the  compensation  has  been  adjusted  to  suit  the 
fundamental  frequency,  it  will  in  general  be  incorrect  for  the 
various  harmonics.  These  instruments  are  designed  for  use 
under  definite  conditions  as  to  voltage,  frequency,  and  wave 
form,  and  though  they  are  serviceable  on  distribution  systems 
where  these  things  are  fixed,  it  is  unsafe  to  apply  them  indis- 
criminately in  general  testing.  The  wattmeters  and  watt-hour 
meters  may  have  very  serious  frequency  and  wave-form  errors, 
especially  at  low  power  factors. 

Use  of  Transformers. — The  use  of  instrument  transformers 
introduces  errors,  due  to  ratio  and  phase  angle,  which  vary 
with  the  load.  These  are  discussed  on  pages  577,  578. 

METHODS  OF  CALIBRATION 

The  dates  of  all  calibrations  should  be  recorded  and  inserted  in 
the  legends  of  the  calibration  plots,  together  with  the  numbers  of  the 
instruments. 


604 


ELECTRICAL  MEASUREMENTS 


Direct-current  Instruments. — As  electrical  measuring  instru- 
ments cannot  be  relied  upon  to  give  absolutely  accurate  results, 
it  is  necessary  to  have  methods  for  calibrating  them.  It  should 
be  possible  to  assemble  the  apparatus  necessary  for  dealing 
with  direct-current  ammeters  and  voltmeters  from  the  instru- 
ments found  in  any  laboratory  devoted  to  general  electrical 
measurements. 

Voltmeter  Calibration  by  Standard  Cell. — The  method  here 
given  is  an  application  of  Poggendorfs  method  (see  page  269). 

An  electromagnetic  voltmeter  is  in  reality  a  galvanometer  in 
series  with  a  high  resistance.  The  scale  of  the  galvanometer  is 
graduated,  not  in  current  strengths,  but  in  the  voltages  which  it 
is  necessary  to  apply  to  the  terminals  of  the  instrument  in  order 
to  obtain  the  various  deflections;  that  is,  in  values  of  IVRV 
where  Iv  and  R v  are  the  current  through,  and  resistance  of,  the 


FIG.  369. — Connections  for  voltmeter  calibration. 


voltmeter.  Therefore,  if  Rv  and  Iv  have  been  measured,  one 
may  find  the  true  value  of  the  P.D.  applied  to  the  instrument, 
and  this  may  be  compared  with  its  nominal  value  as  read  from 
the  scale.  The  difference  will  be  the  correction  to  be  added  to 
the  observed  reading  to  obtain  the  true  value  of  the  P.D. 

The  resistance  of  the  voltmeter  is  determined  by  a  Wheatstone 
bridge. 

The  necessary  connections  for  the  measurement  of  lv  are 
shown  in  Fig.  369. 


THE  CALIBRATION  OF  INSTRUMENTS         605 

B  is  a  battery  capable  of  giving  the  desired  current;  W  is  a 
water  rheostat  by  which  the  current  Iv,  and  consequently  the 
reading  of  the  voltmeter  V,  may  be  varied;  r  is  a  known  and 
variable  resistance.  The  standard  cell  has  a  voltage  denoted  by 
E.  One  must  be  sure  that  the  cell  is  properly  inserted  so  that  in 
the  galvanometer  circuit  its  e.m.f.  will  oppose  the  P.D.  due  to  the 
drop  in  r.  If  the  cell  be  so  inserted  and  Ivr  =  E,  the  galva- 
nometer will  remain  undeflected  when  the  key  K  is  depressed. 

T      -E 
Iv-~ 

and  the  P.D.  across  the  terminals  of  the  voltmeter  will  be  given  by 

P.D.      =     ~RV. 

In  practice  it  is  usually  desired  to  calibrate  at  or  near  certain 
predetermined  points,  at  readings  of  10,  20,  30  volts,  and  so  on. 
It  is,  therefore,  necessary  to  know  the  value  of  r  which  must  be 
inserted  in  order  that  when  the  galvanometer  is  balanced  the 
voltmeter  reading  may  be  that  desired.  This  is  readily  de- 
termined, for  suppose  that  the  instrument  is  to  be  calibrated 
at  or  near  a  reading  of  30  volts,  that  E  =  1.0186  and  Rv  = 
17,000  ohms.  The  proper  value  of  r  would  be, 

1.0186  X  17,000 
r»=  -       — ^TT-       -  =  577  ohms. 

60 

577  ohms  are  to  be  inserted  at  r,  and  by  the  water  rheostat,  W, 
the  reading  of  the  voltmeter  is  to  be  brought  to  30  volts.  It 
may  be  necessary  to  change  the  number  of  battery  cells.  The 
key  K  should  be  depressed  cautiously,  and  released  immediately 
the  deflection  appears.  In  general  there  will  be  a  deflection,  for 
the  voltmeter  will  probably  have  a  slight  error,  so  that  although 
it  reads  30  volts,  the  true  P.D.  between  the  terminals  will  differ 
from  that  value;  also,  the  resistance  r  is  not  exactly  the  value 
corresponding  to  30  volts  for  r  is  adjustable  to  single  ohms  only. 
An  exact  balance  is  obtained  by  varying  the  water  rheostat, 
and  the  voltmeter  is  read  immediately  thereafter.  The  reading 
and  the  corresponding  value  of  r  must  be  recorded.  The  difference 
between  the  true  P.D.  at  the  instrument  terminals  and  the 
reading  gives  the  correction,  the  quantity  which  must  be  added 
to  the  reading  to  obtain  the  true  P.D. 


606 


ELECTRICAL  MEASUREMENTS 


It  is  important  to  take  the  zero  reading,  for  it  is  subject  to 
variation;  and  if  taken  and  separately  allowed  for,  a  calibration 
may  retain  its  value,  if  the  scale  be  equally  divided,  even  though 
the  zero  reading  alter. 

Ammeter  Calibration. — To  calibrate  an  ammeter  it  is  neces- 
sary to  have  a  method  for  measuring  the  current  which  will  be 
free  from  such  instrumental  errors  as  may  affect  the  indications 
of  even  the  best  direct-reading  standard  instruments.  Such 
calibrations  may  be  carried  out  by  the  aid  of  standard  cells  and 
accurately  adjusted  resistances,  as  follows. 


FIG.  370. — Connections  for  ammeter  calibration. 


Referring  to  Fig.  370,  R  is  a  known  resistance  so  constructed 
that  it  will  not  heat  appreciably  with  the  passage  of  the  current. 
This  is  inserted  in  series  with  the  ammeter  to  be  calibrated,  A. 
Rh  is  a  rheostat  for  controlling  the  current,  and  B  is  a  battery  of 
storage  cells  to  furnish  the  steady  current  necessary  in  such 
work. 

To  measure  the  ammeter  current  it  is  necessary  to  determine 
the  P.D.  between  the  potential  terminals  of  R.  This  may  be  done 
by  the  method  of  projection  of  potentials,  an  application  of  Pog- 
gendorff's  method  (page  269).  To  apply  this  it  is  necessary  to 
have  an  auxiliary  battery,  J5i,  of  constant  e.m.f.  and  capable  of 
furnishing  a  small  current,  0.001  amp.,  continuously;  and  two  re- 
sistance boxes,  ri  and  r%,  of  a  total  resistance  of  about  10,000  ohms 


THE  CALIBRATION  OF  INSTRUMENTS         607 

each,  which  should  be  capable  of  adjustment  in  single  ohm 
steps.  In  addition,  a  suitable  galvanometer  and  key  are 
required.  The  wire  ab  causes  the  points  a  and  b  to  assume  the 
same  potential.  If  the  current  through  the  ammeter  be  denoted 
by  7,  the  potential  at  d  differs  from  that  at  a  by  IR.  If  the  poten- 
tial difference  at  the  terminals  of  the  battery  BI  be  P.D.,  that 
between  6  and  c  will  be, 

P.D.  --. 


When  the  potentials  at  c  and  d  are  the  same, 
IR  =  P.D.       T*       > 

r* 

and  if  they  are  the  same,  the  galvanometer  will  not  deflect  when 
the  key  is  depressed.  Consequently,  if  ri  or  r2  has  been  adjusted 
so  that  the  galvanometer  gives  no  deflection, 


R      N  ri  +  r2 

One  cell  of  storage  battery  is  the  most  satisfactory  for  use 
at  BI.  In  order  that  its  P.D.  may  remain  constant,  the  cell 
should  be  partially  discharged.  A  standard  cell  cannot  be  used 
at  BI  because  it  is  incapable  of  supplying  even  a  small  current 
without  alteration  of  its  e.m.f.  through  polarization. 

The  first  step  in'carrying  out  this  test  is  to  determine  the  P.D. 
of  the  auxiliary  battery  B\.  This  is  to  be  done  by  Poggendorff's 
method. 

The  connections  shown  in  Fig.  370  are  then  made;  it  is  neces- 
sary that  BI  and  R  be  connected  +  to  +. 

In  general,  on  closing  the  key  there  will  be  a  deflection  which 
is  to  be  brought  to  zero  by  adjusting  7*1  or  r2.  When  a  balance 
is  obtained,  the  ammeter  is  to  be  read  immediately. 

If  TI  -f  r2  greatly  exceeds  the  battery  resistance  of  BI,  P.D. 
will  be  approximately  the  e.m.f.  of  the  cell.  It  is  well  to  re- 
member that  imperfect  connections  to  the  cell  and  excessive 
lead  resistance  have  the  same  effects  on  the  results  as  high  battery 
resistance  at  BI,  and  that  this  battery  resistance  should  be 
negligible  both  during  the  test  by  Poggendorff's  method  and  the 
subsequent  use  of  the  arrangement  in  determining  the  current. 


608  ELECTRICAL  MEASUREMENTS 

By  using  proper  resistances  at  R,  currents  of  all  magnitudes  can 
be  measured  by  this  method. 

Calibration  by  Means  of  Potentiometer. — Direct-current 
ammeters  and  voltmeters  are  most  readily  calibrated  by  means 
of  the  ordinary  or  the  deflectional  type  of  potentiometer.  Cur- 
rents are  determined  by  measuring  the  P.D.  between  the 
terminals  of  standard  resistances.  These  resistances  should  be 
certified  by  the  Bureau  of  Standards.  This  should  be  done  once 
a  year,  since  the  resistances  are  subject  to  slight  changes. 

For  voltage  measurements,  the  range  of  potentiometers  may 
be  extended  upward  from  1.5  volts  to  any  desired  extent  by  the 
use  of  volt  boxes. ' 

As  a  source  of  current  for  ammeter  calibrations,  a  4-volt  storage 
battery  is  most  convenient.  The  cells  may  be  charged  in  series 
and  discharged  in  parallel.  Variations  in  the  current  are 
obtained  by  the  use  of  rheostats.  These  may  have  metal  grids 
for  the  large  steps  and  a  carbon  compression  rheostat  for  the  fine 
adjustments. 

For  potential  differences  a  storage  battery  should  also  be  em- 
ployed. The  cells  must  be  large  enough  so  that  they  may 
be  properly  taken  care  of.  A  drop  wire  furnishes  the  most 
convenient  means  of  regulating  the  P.D.  at  the  instruments. 

Alternating-current  Ammeters  and  Voltmeters. — The  larger 
part  of  the  alternating-current  voltmeters  in  daily  use  for  engineer- 
ing work  are  based  on  the  electrodynamometer  principle.  Such 
instruments  may  be  calibrated  with  direct  currents,  using  either 
a  standard  direct-current  voltmeter,  whose  errors  are  accurately 
known,  or  a  direct-current  potentiometer  and  volt  box.  On 
account  of  the  effect  of  the  local  field,  it  is  essential  that  two  read- 
ings be  taken  at  each  point,  first  with  a  voltage  in  a  noted  direc- 
tion, and  then  with  it  reversed.  The  two  results  should  be 
averaged.  This  procedure  ignores  the  existence  of  any  fre- 
quency error.  The  magnitude  of  this  error  may  be  calculated 
from  the  measured  inductance  and  resistance  of  the  instrument. 

Except  in  the  case  of  the  thermal  instruments,  which  give  the 
same  reading  with  both  direct  and  alternating  currents,  and 
regular  electrodynamometers,  with  the  two  coils  in  series,  it  is 
necessary  to  -use  alternating  currents  when  calibrating  alternat- 
ing-current ammeters;  for  generally  they  are  soft-iron  instru- 


THE  CALIBRATION  OF  INSTRUMENTS 


609 


ments,  whose  indications  on  direct-current  circuits  are  compli- 
cated by  the  effects  of  residual  magnetism  in  the  iron  vane. 
Also  there  may  be  errors  due  to  wave  form.  These  same  remarks 
apply  to  soft-iron  voltmeters  which  are  intended  for  alternating 
currents.  Induction  ammeters  and  voltmeters  must  be  cali- 
brated with  alternating  current. 

The  calibrations  may  be  made  by  the  alternating-current 
potentiometer,  used  in  connection  with  non-reactive  volt  boxes 
and  shunts,  but  this  instrument  is  not  yet  in  common  use. 
It  would  not  be  serviceable  if  wave-form  errors  were  being 
investigated. 

The  arrangement  shown  in  Fig.  371  does  very  well  for  ammeters. 


220  Volts 


Transfer  Inst, 

Hot  Wire  Ammeter 

and  Shunts 

FIG.  371. — Connections  used  in  calibrating  alternating-current  ammeter. 

The  hot-wire  ammeter,  provided  with  an  appropriate  set  of 
shunts,  is  used  as  a  transfer  instrument.  The  ammeter  under 
calibration  is  compared  with  it,  and  then  by  means  of  the  double- 
throw  switch  the  hot-wire  instrument  is  transferred  to  the  direct- 
current  circuit  and  calibrated  at  the  proper  point  by  means  of  a 
potentiometer  and  standard  resistances.  This  procedure  avoids 
all  questions  as  to  the  permanence  of  the  calibration  of  the  hot- 
wire instrument.  A  difficulty  is  that  the  range  of  a  hot-wire 
ammeter  is  short,  the  deflection  depending  upon  the  square  of 
the  current.  Consequently,  the 'scale  is  of  such  a  nature  that 
even  with  care  only  about  the  upper  60  per  cent  of  it  is  readable 
with  sufficient  accuracy.  Therefore  the  millivoltmeter  part 
should  be  sensitive,  and  the  range  extended  by  numerous  shunts, 
so  that  the  deflection  may  be  kept  in  the  upper  part  of  the  scale. 

•Soft-iron  voltmeters  may  be  compared  with  a  dynamometer 
instrument  which  has  been  calibrated  with  direct  current. 

39 


610  ELECTRICAL  MEASUREMENTS 

Northrup    Alternating-    and    Direct-current    Comparator.— 

The  indicating  portion  of  the  Northrup  comparator  may  be  de- 
scribed as  a  differential  hot-wire  millivoltmeter  (or  milliammeter). 
The  general  features  of  its  construction  will  be  evident  from 
Fig.  372.  The  "hot  wires"  are  shown  at  a,  d,  c,  and  a',  d',  c'; 
they  are  supposed  to  be  of  the  same  diameter,  resistance,  and 
coefficient  of  expansion,  and  to  be  placed  in  similar  environments. 
They  are  placed  in  a  horizontal  position,  and  shielded  from  all 
drafts  by  a  suitable  case. 


FIG.  372. — Diagram  for  Northrup  comparator. 

At  the  middle  of  their  lengths  they  are  connected  by  an  insu- 
lating bridge  piece,  which  carries  a  mirror  and  is  drawn  down- 
ward by  a  spring,  so  that  both  wires  are  taut.  A  telescope  and 
scale  are  used  to  observe  the  angular  deflection  of  the  mirror. 
In  the  ideal  case,  if  the  same  current  flows  through  the  two 
wires,  they  heat  and  therefore  expand  equally.  In  this  case  the 
mirror  moves  back  a  little  without  being  tilted,  and  the  scale 
reading  is  unchanged.  If,  however,  the  currents  are  not  the 
same,  the  wires  are  heated  and  expand  unequally,  and  a  deflec- 
tion will  be  observed,  which  may  be  reduced  to  zero  by  altering 
one  of  the  currents.  When  the  instrument  is  in  use  one  wire  is 
traversed  by  direct,  the  other  by  alternating  current,  and  a 
means  is  thus  afforded  of  telling  when  the  currents  are  of  equal 
strengths.  After  the  currents  have  been  adjusted  to  equality, 
the  direct  current  is  measured  by  any  convenient  and  accurate 
means.  With  the  appropriate  auxiliary  devices,  the  com- 
parator may  be  used  for  the  calibration  of  alternating-current 
ammeters  and  voltmeters. 

Wattmeters. — When  two  wattmeters  are  to  be  compared,  the 
current  coils  are  placed  in  series  and  the  potential  coils  in  parallel. 
If  both  instruments  are  of  the  dynamometer  type  direct  current 
may  be  used,  reversals  being  taken  to  eliminate  the  effects -of 
the  local  field, 


THE  CALIBRATION  OF  INSTRUMENTS 


611 


When  calibrating  high-capacity  wattmeters,  in  order  to  save 
power  and  bring  the  work  within  the  range  of  the  apparatus 
found  in  a  well-equipped  laboratory,  it  is  necessary  to  resort  to 
fictitious  loading;  that  is,  to  supplying  the  current  and  potential 
coils  from  two  distinct  sources. 

The  connections  for  a  calibration  are  then  as  shown  in  Fig.  373. 

It  is  convenient  to  use  storage  cells  for  supplying  both  the 
current  and  potential  circuits.  Two  readings  are  made  at  each 
point,  both  the  current  and  the  potential  switches  being  reversed. 
The  results  are  averaged  to  eliminate  the  effect  of  the  local  field. 


To 
Volti 


or 

Potentiometer 

/    1 

^ 

-0           0- 

To  be 
Tested 

FIG.  373. — Connections  for  fictitious  loading  of  wattmeter. 

In  this  procedure  eddy  current  and  frequency  errors  are 
assumed  to  be  negligible.  If  there  is  doubt  as  to  this,  the  watt- 
meter must  be  compared  with  one  known  to  be  free  of  them 
using  alternating  currents  of  the  proper  frequency. 

If  an  induction  meter  is  being  tested,  alternating  current  of  the 
proper  frequency  must  be  used  and  the  instrument  compared 
with  an  electrodynamometer  wattmeter  which  has  been  calibrated 
with  direct  current. 

In  case  it  is  necessary  to  test  at  different  power  factors,  the 
supply  may  be  derived  from  two  alternating-current  machines, 
having  the  same  number  of  poles,  with  their  armatures  on  the 
same  shaft,  one  field  being  arranged  so  that  it  may  be  given  any 
desired  angular  displacement  about  the  axis  of  rotation.  The 
wave  form  of  both  machines  should  be  sinusoidal.  A  phase 
shifting  transformer  (see  page  290)  may  also  be  used  and  is 
more  convenient. 

Reference 

"Testing  of  Electrical  Measuring  Instruments,"  Circular  No.  20,  U.  S. 
Bureau  of  Standards. 


CHAPTER  XIV 
DETERMINATION  OF  WAVE  FORM 

To  simplify  the  mathematical  treatment  of  the  flow  of  alternat- 
ing currents,  it  is  customary  to  assume  that  both  the  applied 
e.m.f.  wave  and  the  current  wave  are  sinusoidal. 

Designers  now  aim  to  produce  machines  with  e.m.f.  waves 
which  are  sinsuoidal,  or  nearly  so,  since  experience  has  shown 
that,  all  things  considered,  this  form  of  e.m.f.  wave  is  the  most 
advantageous  in  practice.  As  an  illustration,  modern  metering 
devices,  upon  whose  indications  the  charges  for  electric  service 
are  based,  will  not  give  results  which  are  commercially  correct 
if  the  wave  form  is  badly  distorted  so  that  it  differs  greatly  from 
a  sinusoid. 


A 

FIG.  376. — Examples  of  wave  forms. 

Fig.  376,  A,  shows  the  e.m.f.  wave  of  a  modern  turbo-alternator. 
The  departure  from  the  sinusoidal  form  is  not  obvious  and  a  care- 
ful analysis  must  be  made  before  one  can  state  what  it  is.  On 
the  other  hand,  Fig.  376,  B,  shows  the  e.m.f.  wave  of  a  much  older 
type  of  machine;  such  a  wave  form  might  seriously  complicate  the 
behavior  of  the  devices  placed  in  circuit. 

The  form  of  the  current  wave  is  affected  by  the  character  of 
the  circuit.  If  the  e.m.f.  wave  is  not  a  pure  sine  curve,  the  effect 
of  its  various  harmonics  in  the  current  wave  will  be  accentuated 
by  capacity  and  smoothed  out  by  inductance  in  the  circuit. 

Saturation  effects  in  iron  cores  may  also  materially  affect 
the  form  of  the  current  wave.  This  is  illustrated  in  Fig.  377, 

612 


DETERMINATION  OF  WAVE  FORM  613 

which  shows  the  potential  difference  applied  to  and  the  current 
in  a  coil  with  an  iron  core. 

In  engineering  work,  cases  are  continually  arising  where  wave 
form  determinations  are  of  the  utmost  importance  on  account  of 
the  assistance  they  give  in  explaining  the  behavior  of  electrical 
apparatus. 

Two  cases  may  arise: 

A.  When  the  phenomena  are  periodic;  for  instance,  the  ordi- 
nary electromotive  force  and  current  waves,  Fig.  377. 


FIG.  377. — Potential  difference  applied  to  and  current  in  a  coil  with 

iron  core. 

B.  When  the  phenomena  are  transient;  such  as  those  occurring 
when  the  circuit  conditions  are  suddenly  altered.  This  is  illus- 
trated by  Fig.  394,  which  shows  the  potential  difference  and 
current  curves  taken  during  a  short  circuit  test  of  an  enclosed 
fuse. 

Contact  Method  for  Determining  Wave  Forms.1 — Methods 
for  dealing  with  case  A  were  first  developed,  the  earliest  being 
the  contact  method,  used  in  1849  by  Lenz  in  investigating  the 
wave  forms  of  alternators.  In  1880  Joubert  employed  it  to 
determine  the  wave  form  of  a  Siemens  machine  and  since  then 
it  has  commonly  been  called  Joubert's  contact  method. 

The  fundamental  idea  is  to  connect  periodically  the  measur- 
ing apparatus  to  the  circuit  for  a  time  so  short  that  during  it  the 
current  or  voltage  remains  practically  unchanged.  This  is 
accomplished  by  an  apparatus  which  is  the  equivalent  of  a  key 
operated  by  a  rigid  connection  from  the  dynamo  shaft.  The 


614 


ELECTRICAL  MEASUREMENTS 


key  is  closed  for  an  instant  once  during  each  revolution  of  the 
dynamo,  and  at  a  definite  point  on  the  wave. 

If  the  voltage  is  high,  a  large  non-reactive  resistance,  R,  Fig. 
378,  is  placed  across  the  circuit,  and  by  means  of  a  tap  a  definite 
fraction  of  the  total  voltage  is  impressed  on  the  apparatus. 

Referring  to  Fig.  378,  the  contact  wheel  of  hard  rubber  or 
fiber  is  at  W.  In  the  original  arrangement  this  wheel  was  at- 
tached directly  to  the  dynamo  shaft;  BI  is  a  brush  which  rests  on 
a  collector  ring  and  gives  permanent  connection  to  the  contact 
point  P,  which  projects  very  slightly  from  the  periphery  of  the 
wheel,  W.  B%  is  a  thin  and  very  light  brush  which  rests  on  the 


Mains 
R,L=0 


b'    a' 


D.C. 

Calibrating 
Circuit 


FIG.  378. — Connections  for  contact  method  for  wave  form,  using  quadrant 

electrometer. 

contact  wheel.  It  is  supported  from  a  movable  brush  holder 
which  may  be  set  at  any  desired  position  along  a  uniformly 
graduated  arc,  AC. 

The  .measurements  may  be  made  by  the  aid  of  an  electrostatic 
voltmeter,  a  quadrant  electrometer  or  a  ballistic  galvanometer. 
In  the  arrangements  shown  in  Fig.  378  the  needle  of  the  electro- 
meter is  kept  charged  to  a  high  potential  by  the  battery  and 
consequently  the  deflection  is  sensibly  proportional  to  the  applied 
voltage;  that  is,  to  the  potential  difference  between  a  and  b  at 
the  instant  of  contact.  The  well-insulated  condenser,  C,  adds 
to  the  capacity  of  the  electrometer  so  that  the  voltage  on  the 
instrument  will  not  be  appreciably  altered  by  leakage  during  the 
time  between  the  successive  contacts  of  B2  and  P. 

The  process  is  to  set  the  brush  at  a  definite  position  on  the  arc 
and  to  read  the  electrometer;  then  to  move  the  brush  forward 
to  another  position  and  take  another  reading,  and  so  on. 


DETERMINATION  OF  WAVE  FORM 


615 


The  magnitude  of  the  deflections  may  be  controlled  by  means 
of  the  battery  and  the  resistance  ba. 

The  electrometer  is  calibrated  by  use  of  direct-current  voltages 
as  indicated. 


329 


Readings  on  Arc 


FIG.  379. — Wave  form  determined  by  contact  method. 

The  electrometer  readings,  reduced  to  volts,  are  plotted  against 
the  readings  on  the  uniformly  graduated  arc,  as  shown  in  Fig.  379, 
and  a  smooth  curve  drawn  through  the  points. 

If  an  electrostatic  voltmeter  is  used  in  place  of  the  electro- 
meter, a  difficulty  is  encountered,  since  the  deflections  depend 
on  the  square  of  the  voltage ;  hence  those  obtained  near  the  zero 


FIG.  380. — Contact  method  for  wave  form,  using  ballistic  galvanometer. 

points  of  the  wave  will  be  very  small.  This  difficulty  may  be 
obviated  by  working  from  a  false  zero.  A  battery  of  sufficient 
voltage  to  give  a  large  deflection  is  joined  in  series  with  the  volt- 
meter ;  thus  when  readings  are  taken  the  voltage  to  be  measured 


616  ELECTRICAL  MEASUREMENTS 

is  superposed  on  the  battery  voltage.  If  a  reflecting  instrument 
is  used,  the  calibration  curve  is  very  closely  a  parabola,  and  as 
the  upper  part  of  it  is  practically  a  straight  line  the  deflection 
from  the  false  zero  is  sensibly  proportional  to  the  voltage  between 
a  and  b  at  the  instant  of  contact. 

Fig.  380  shows  the  arrangement  when  a  ballistic  galvanometer 
is  employed. 

In  this  arrangement  Si  is  a  double-pole,  double-throw  switch, 
by  which  the  apparatus  may  be  connected  to  the  alternating- 
current  circuit,  or  to  the  direct- current  circuit  for  purposes  of 
calibration.  C\  is  a  variable  condenser  which  is  charged  by 
throwing  S2  to  the  left,  and  discharged  through  the  ballistic 
galvanometer,  BG,  when  the  switch  is  thrown  to  the  right. 

The  deflection,  which  is  proportional  to  the  instantaneous 
voltage  between  a  and  b,  may  be  controlled  by  varying  the 
capacity. 

Use  of  Potentiometer  Principle. — These  methods  may  be 
improved  upon  if  a  potentiometer  arrangement  is  adopted,  as 
shown  in  Fig.  381. 


B 

FIG.  381. — Contact  method  for  wave  form,   using  potentiometer 

principle. 

Referring  to  the  figure,  DE  is  a  slide  wire,  or  its  equivalent, 
which  is  supplied  with  direct  current  from  B.  The  voltage  from 
0  to  D  or  E,  is  slightly  larger  than  the  maximum  occurring  be- 
tween a  and  b.  A  direct-current  voltmeter  is  connected  between 
0  and  the  slider  S;  G  is  a  detector,  which  may  be  a  telephone 
or  a  •  moving-coil  galvanometer;  a  Kelvin  instrument  is  not 
suitable. 

After  setting  the  contact  brush,  the  position  of  the  slider  S 
is  varied  until  the  detector  G  stands  at  zero.  The  instantaneous 


DETERMINATION  OF  WAVE  FORM  617 

voltage  between  a  and  b  is  then  equal  to  the  steady  voltage 
between  0  and  S,  and  the  latter  is  read  from  the  direct-current 
voltmeter. 

The  methods  given  are  applied  to  current  waves  by  placing  a 
non-reactive  resistance  (shown  at  a'b')  directly  in  the  circuit 
and  determining  the  instantaneous  potential  differences  between 
its  terminals. 

The  time  consumed  in  mapping  a  wave  form  .by  the  foregoing 
methods  is  considerable;  in  itself  this  is  disadvantageous,  and 
it  also  necessitates  holding  the  circuit  conditions  practically  con- 
stant for  a  considerable  time,  for  if  the  wave  is  non-sinusoidal, 
many  points  near  together  must  be  taken.  Frequently  in 
industrial  testing  the  conditions  cannot  be  maintained  constant. 
In  addition,  much  time  and  labor  must  be  expended  in  computing 
and  plotting  the  results.  Obviously,  simultaneous  records  of 
two  or  more  waves  cannot  be  obtained  with  a  single  instrument. 

In  many  cases  the  necessity  for  directly  connecting  the  con- 
tact disc  to  the  dynamo  shaft  practically  prohibits  the  use  of  the 
contact  method  in  the  forms  previously  given,  for  it  is  frequently 
necessary  to  determine  the  wave  forms  at  a  place  which  may  be 
at  a  considerable  distance  from  the  generating  station. 

From  the  potentiometer  method,  the  Rosa  curve  tracer, 
shown  in  Fig.  382,  has  been  developed.  The  object  of  this 
machine  is  to  reduce  the  time  necessary  for  making  the 
observations  and  plotting  the  results.  In  Fig.  381,  if  the  direct- 
current  voltmeter  is  omitted,  and  the  potentiometer  wire  carries  a 
definite  current,  the  displacement,  OS,  of  the  slider  from  the  zero 
position  will,  at  balance,  be  proportional  to  the  instantaneous 
voltage.  The  idea  is  to  plot  these  displacements,  as  ordinates, 
on  a  sheet  of  paper  carried  by  a  drum,  the  abscissae  being  pro- 
portional to  the  displacements  of  the  contact  brush  along  the 
arc  AC.  This  is  done  in  a  semi-automatic  manner,  as  will  be 
seen  from  the  following. 

Referring  to  Fig.  382,  the  potentiometer  wire,  DE,  in  Fig. 
381,  is  wound  in  a  screw  thread  on  an  ebonite  cylinder.  When 
the  cylinder  is  turned,  another  thread  of  the  same  pitch  cut  in 
the  ebonite,  serves  to  move  the  carriage  to  which  are  attached 
the  contact  point,  8,  and  the  stile  for  registering  the  results. 

A  short-period,  dead-beat,  moving-coil  galvanometer  is  used 


618 


ELECTRICAL  MEASUREMENTS 


as  a  detector.  To  make  an  observation,  the  handle  at  the  right 
is  turned  until  the  galvanometer  stands  at  zero.  Then  the  lever 
at  the  left  is  raised,  causing  the  stile,  through  the  medium  of 
the  typewriter  ribbon,  to  imprint  a  dot  on  the  paper  which  is 
carried  by  the  large  drum  at  the  rear  of  the  apparatus.  When  the 
lever  is  lowered,  a  ratchet  and  pawl  turn  the  drum  a  prede- 
termined amount,  and  at  the  same  time,  by  means  of  another 
pawl  and  ratchet,  actuated  by  an  electromagnet,  the  contact 
brush,  B2,  in  Fig.  381,  is  advanced  proportionally. 


FIG.  382. — Potentiometer  and  registering  apparatus  for  Rosa  curve  tracer. 

The  teeth  of  the  ratchets  of  the  contact  maker  and  of  the  drum 
are  numbered  correspondingly,  so  that  the  brush  and  the  record- 
ing drum  may  be  set  at  any  desired  position.  As  shown  in  Fig. 
383,  the  points  may  be  taken  close  together,  so  that  irregular 
waves  may  be  dealt  with. 

For  the  best  work,  it  is  necessary  to  connect  the  contact  wheel 
directly  to  the  dynamo  shaft  and  to  keep  the  circuit  conditions 
perfectly  constant.  If  this  can  be  done,  the  Rosa  curve  tracer 
furnishes  the  most  accurate  apparatus  yet  devised  for  mapping 
periodic  electrical  phenomena.  There  are  other  modifications 
of  the  contact  method  which  reduce  the  time  necessary  for  record- 
ing the  waves  and  give  results  sufficiently  accurate  for  much 


DETERMINATION  OF  WAVE  FORM 


619 


engineering  work.     These  devices  are  made  self-registering.     In 
that  shown  in  Fig.  384  the  trace  is  recorded  photographically.2 

The  necessary  electrical  connections  are  shown  in  Fig.  385. 
KI  and  K2  are  two  rigidly  connected  contact  wheels  of  ebonite. 


.-.D  .- 


•B    .. 


.'A 


Curve  A,  Electromotive  Force  Wave.    Curve  B,  Current  Wave. 
Resonance  of  Fifteenth  Harmonic 

FIG.  383. — Wave  form  taken  with  Rosa  curve  tracer. 

Into  the  periphery  of  each  wheel  are  set  four  brass  blocks  which 
are  placed  90°  apart.  Upon  each  wheel  a  brush  and  a  collector 
ring  give  permanent  contact  with  all  the  blocks.  Another 
brush,  resting  on  the  periphery  of  the  wheel,  completes  the 


FIG.  384. — Synchronous  commutator  with  continuously  moving  brushes, 
for  use  in  determining  wave  form. 

electrical  connection  as  the  blocks  pass  under  it.  The  brushes 
are  so  set  that  contact  is  made  and  broken  at  Kz  before  KI 
closes.  The  contact  wheels  are  driven  by  a  synchronous  motor, 
which  makes  one  revolution  for  four  complete  cycles  of  the 


620 


ELECTRICAL  MEASUREMENTS 


e.m.f.  G  is  a  dead-beat  galvanometer,  and  C  is  an  adjustable 
condenser.  The  leads  a  and  b  are  carried  to  the  points  between 
which  the  P.D.  is  to  be  investigated.  By  inspection  of  the 
diagram  it  will  be  seen  that  once  on  each  wave,  and  at  a  definite 
point,  the  condenser  C  is  charged  to  the  potential  existing  be- 
tween a  and  b.  As  the  charge  is  determined  by  the  breaking  of 
the  contact,  the  blocks  may  be  of  sufficient  width  to  eliminate 
the  effect  of  the  jumping  of  the  brushes.  Also  the  resistance  at 
the  contact  will  not  be  of  sufficient  magnitude  to  prevent 
complete  charging  of  the  condenser. 


FIG.  385. — Connections  for  synchronous  commutator. 

The  function  of  KI  is  to  discharge  the  condenser  through  the 
galvanometer  after  K2  has  broken  circuit.  The  instrument 
would  ordinarily  experience  a  constant  deflection,  but  the 
brushes  KI  and  K2  are  rigidly  connected  and  mounted  on  a 
radial  arm,  which  is  geared  to  the  shaft  so  that  it  moves  very 
slowly.  The  effect  is  to  gradually  move  the  contact  point  over 
the  wave.  The  deflection  of  the  galvanometer  will  at  any  instant 
be  proportional  to  the  P.D.  between  a  and  b  at  the  instant  of 
breaking  at  Kz,  or  in  other  words,  the  deflection  follows  the 
wave  form. 

The  actual  arrangement  is  shown  in  Fig.  384,  where  the  con- 
tact device,  the  synchronous  motor,  and  the  direct-current  motor 
used  for  starting  the  apparatus  will  be  seen.  By  use  of  worm 
gearing  the  wheel  train  necessary  for  moving  the  brushes  is 
made  very  compact;  the  reduction  for  the  instrument  shown  is 
7,200  to  1. 


DETERMINATION  OF  WAVE  FORM 


621 


A  dead-beat  galvanometer  with  a  good  law  of  deflection  and 
a  well-defined  zero  is  used. 

The  record  is  made  on  a  photographic  plate  which  is  moved 
vertically  by  a  fine  wire  wound  on  a  drum,  seen  in  Fig.  384,  just 
in  front  of  the  lower  worm-wheel.  This  drum  can  be  thrown  in 
gear  by  a  pin  clutch. 


FIG.  386. — General  Electric  Co.  wave  meter. 

The  adjustable  condenser  allows  one  to  adapt  the  apparatus 
to  varying  conditions,  so  the  e.m.f.  curves  may  be  taken  directly, 
and  the  current  curves  by  the  use  of  a  drop  wire,  as  indicated  in 
Fig.  385. 

The  General  Electric  Co.'s  wave  meter5  is  in  effect  similar 
to  the  above  device.  The  motion  of  the  brushes  and  of  the  pho- 


622 


ELECTRICAL  MEASUREMENTS 


tographic  plate  is  obtained  by  a  falling  weight  and  controlled  by 
means  of  the  dash  pot  on  the  pillar  below  the  plate  holder,  so 
that  the  desired  speed  of  the  contact  brushes  may  be  obtained. 


FIG.  387. — Hospitaller  ondograph. 

The   Hospitalier   ondograph,2   Fig.   387,   is  another    arrange- 
ment of  the  same  sort.    By  means  of  a  pen  actuated  by  a  special 


DETERMINATION  OF  WAVE  FORM 


623 


dead-beat  moving  coil  galvanometer  of  high  torque  the  curve 
is  drawn  on  a  sheet  of  paper  carried  by  a  revolving  drum. 

Referring  to  Fig.  387,  two  brushes  are  in  metallic  connection 
when  they  simultaneously  rest  on  the  unshaded  portion  of  the 


.1: 


FIG.  388. — Pen  mechanism  of  Hospitaller  ondograph. 

commutator;  the  figure,  therefore,  shows  the  connections  when 
the  condenser  is  discharging  through  the  galvanometer.  The 
condenser  will  be  charged  when  d  and  d'  both  rest  on  the  un- 
shaded part  of  the  commutator,  the  galvanometer  connection 
then  being  broken. 


FIG.  389. — Record  obtained  by  Hospitalier  ondograph. 

The  apparatus  is  driven  by  a  small  synchronous  motor  with 
four  poles,  so  geared  to  the  commutator  that  the  latter  makes 
999  revolutions  while  the  motor  makes  1,000.  The  result  is 
that  with  each  revolution  the  brushes,  though  stationary,  are 


624 


ELECTRICAL  MEASUREMENTS 


in  effect  shifted  slightly  with  respect  to  the  wave  form,  and  the 
charge  given  to  the  condenser  varies  accordingly.  The,,  result 
is  the  same  as  that  attained  in  the  previous  apparatus  by  shifting 
the  brushes. 

The  recording  drum  is  geared  to  make  one  complete  turn 
while  the  motor  makes  1,500  revolutions,  so  that  three  waves 
are  recorded  per  revolution  of  the  drum.  The  pen,  if  attached 
directly  to  the  index  of  the  galvanometer,  would  move  on  so 
short  a  radius  that  the  diagram  would  be  much  distorted.  This 
distortion  is  reduced  in  the  manner  indicated  in  Fig.  388. 

The  arm,  db,  18  cm.  long,  is  attached  to  the  movable  system; 
by  means  of  a  fork  it  turns  the  arm,  ec,  36  cm.  long  and  pivoted 
at  e.  This  arm  carries  the  pen  at  c.  The  arc  ac  is  much  nearer 
a  straight  line  than  is  db  and  its  length  is  proportional  to  6. 

The  record  obtained  is  shown  in  Fig.  389.  The  fact  that  it 
is  not  on  rectangular  coordinates  is  a  disadvantage,  especially  if 
it  is  desired  to  analyze  the  waves. 


Vm. 


FIG.  390. — Connections  for  integrating  method  for  determining  wave  form. 

Integrating  Methods  for  Determining   Wave   Form.3 — One 

arrangement  for  determining  wave  form  by  an  integrating 
method  rather  than  by  "  instantaneous "  contacts  is  shown  dia- 
grammatically  in  Fig.  390. 

The  current,  i\,  whose  wave  form  is  to  be  determined  passes 
through  the  primary  of  an  air-core  transformer,  in  the  secondary 
of  which  is  a  low-range  voltmeter,  or  a  galvanometer,  and  the 


DETERMINATION  OF  WAVE  FORM  625 

commutator,  D.  The  commutator  is  driven  from  the  dynamo 
shaft  or  by  a  synchronous  motor  and  is  so  constructed  that  the 
connections  to  the  galvanometer  are  reversed  at  each  half  wave. 
As  shown  in  the  figure,  the  commutator  is  suitable  for  a  two-pole 
machine;  if  there  are  more  poles,  it  is  merely  necessary  to  increase 
the  number  of  segments  correspondingly. 

The  distance  between  the  brushes  is  180  electrical  degrees. 
They  are  mounted  in  a  holder  which  can  be  moved  concentrically 
with  the  shaft  so  that  they  may  be  set  at  any  point  on  the  wave. 
Their  position  can  be  read  from  a  graduated  circle.  It  is  con- 
venient to  have  the  arrangement  such  that  the  brushes  can 
readily  be  moved  in  a  succession  of  equal  steps.  Thin  metallic 
brushes  which  will  not  short-circuit  the  commutator  should  be 
used.  The  apparatus  must  be  well-insulated  to  prevent  the 
entrance  of  stray  currents.  This  form  of  commutator  is  applic- 
able only  when  the  two  halves  of  the  wave  are  alike  (except 
for  algebraic  sign),  that  is,  when  only  odd  harmonics  are  present. 

The  galvanometer  should  be  of  the  moving-coil  type  and  one 
which  correctly  integrates  a  transient  current. 

When  the  commutator  is  in  action  the  galvanometer  experi- 
ences a  deflection  which  is  proportional  to  the  average  value  of 
the  current  during  a  half  cycle.  The  reading  of  the  instrument, 
72,  is  given  by 


Let  R  =  resistance  of  secondary  circuit  of  transformer. 
m  =  mutual  inductance  of  transformer. 

/    =  frequency. 

ez  =  instantaneous  induced  e.m.f.  in  secondary. 

¥2  =  reading  of  voltmeter. 

ii    =  instantaneous  current  in  primary. 

iz    =  instantaneous  current  in  secondary. 

7  2    =  average  value  of  current  in  secondary. 
Then  dii 


m 

40 


T  T  T 

p+s     p  +  r         p.+  r     T 

I  dii  =    I   e^dt  =  R  I  i%dt  =  ~  RI 

J,      J,         J«       2 


626  ELECTRICAL  MEASUREMENTS 

T 

.'.  2m(ii)t  =  ^RI2 
& 

(ii)t  =     . ,       =  ~77r—  =  K  times  the  scale  reading: 

K  is  a  constant  of  the  instrument.  This  gives  the  instantaneous 
value  of  the  current  at  a  particular  point  on  the  wave,  and  the 
form  is  traced  point  by  point  as  in  the  contact  method. 

E.m.f.  Waves. — Electromotive  force  waves  are  obtained  by 
placing  the  primary  of  a  suitable  air-core  transformer  in  series 
with  a  high  non-reactive  resistance,  which  is  across  the  line.  If 
the  resistance  is  so  high  that  the  circuit  is  practically  non- 
reactive,  a  determination  of  the  form  of  the  current  wave  in  it 
gives  the  wave  form  for  the  potential  difference  applied  to  its 
terminals.  As  the  resistance  must  be  large,  the  method  is  not 
applicable  to  low  voltages. 

With  this  arrangement  all  'the  measuring  apparatus  is  entirely 
separated  from  the  primary  circuit.  This  may  be  advantageous 
if  the  voltage  is  high. 

The  transformer  should  have  a  variable  ratio.  If  the  mutual 
inductance  is  not  known,  the  apparatus  may  be  calibrated  by 
use  of  a  sinusoidal  current.  The  maximum  ordinate  may  then 
be  calculated  from  the  measured  value  of  the  current,  and  com- 
pared with  the  reading  of  the  galvanometer,  72. 

Or,  a  wave  may  be  plotted,  using  the  readings  of  the  galvan- 
ometer, its  root-mean-square  computed,  and.  this  compared  with 
the  same  quantity  determined  by  a  standard  alternating-current 
ammeter. 

Flux  Waves. — Referring  to  Fig.  390  the  flux  which  threads 
the  secondary  is  at  every  instant  proportional  to  the  current  in 
the  primary,  the  wave  form  of  which  has  been  determined.  Thus 
the  form  of  this  flux  curve  has  also  been  found.  The  total  flux 
through  the  secondary  at  any  instant  will  be  (ii)tm. 

This  suggests  that  in  case  the  form  of  a  flux  wave  is  desired, 
it  is  only  necessary  to  replace  the  secondary  of  Fig.  390  by  a  coil 
of  N  turns  wound  around  the  core,  through  which  the  flux  passes. 

For  the  case  considered  above  the  total  flux  linkages  at  any 
instant,  t,  is  given  by 

F2 
w(*i)<  =  47- 


DETERMINATION  OF  WAVE  FORM  627 

In  the  case  under  consideration,  the  flux  through  the  core  is 


4/W 


2 
(v)>  =  - 


Or  if  F2  is  in  volts, 


.  If  a  non-synchronous  commutator  is  used,  the  maximum  value 
of  the  flux  will  be  proportional  to  the  maximum  reading  of  the 
voltmeter,  as  it  goes  through  its  cycle  of  deflections. 

Use  of  Condenser  and  Synchronous  Commutator. — Another 
arrangement  for  determining  the  forms  of  potential  waves  is 


FIG.  391. — Connections  for  determining  wave  form  by  synchronous  com- 
mutator and  condenser. 

shown  in  Fig.  391.  Here  a  condenser,  the  commutator  and  a 
galvanometer,  or  a  millivoltmeter,  are  joined  in  series  across 
the  mains. 

The  current  through  the  circuit  is  i  =  ^7.     In  half  a  cycle 

the  charge  on  the  condenser  changes  from  -\-q  to  —  q,  so 

T 
2 


r*  -  Q      /*«  + 
I  dq  =    I  idt 

J  +5  Jt 


The  reading  of  the  galvanometer,  7,  is  proportional  to  the  average 
current,  or  _  .  T  ~  •  T. 

I  =  ~,\idt  =  2f  \  idt 


2f  +  *          f 
=  7p  I  idt  =  2f  I  idt 


•'•  *«  =  27 

But  if  a  good  condenser  is  used,  q  =  VtC, 
so  I 


628 


ELECTRICAL  MEASUREMENTS 


The  deflection  may  be  controlled  by  varying  C.  Currents  may 
be  dealt  with  in  the  usual  way  by  determining  the  P.D.  between 
the  terminals  of  a  non-reactive  resistance  through  which  the 
current  flows. 

Determination  of  the  Average  Values  of  Potential  Difference 
and  Current  Waves. — If  the  commutator  is  arranged  as  in  Fig. 
392,  average  values  of  the  potential  difference  and  current  may 
be  determined.  To  do  this  the  brushes  must  be  so  set  that  the 
reversals  are  at  the  zero  points  of  the  wave.  When  the  switch 


FIG.  392. — Connections  for  determining  average  value  of  alternating-cur- 
rent wave. 

is  on  1  the  galvanometer  is  subjected  to  a  series  of  unidirectional 
impulses  and  gives  a  deflection  proportional  to  their  average 
value.  The  instrument  may  be  calibrated  by  transferring  it  to 
the  line  side  of  the  commutator  and  applying  a  known  direct- 
current  voltage. 

To  properly  set  the  brushes  the  switch  is  placed  on  2  so  that  the 
condenser  C  is  in  circuit  and  the  position  of  the  brushes  altered 
until  the  galvanometer  stands  at  zero.  Currents  are  dealt  with 
by  using  a  non-reactive  resistance  as  in  the  previous  method. 


Cone. 


FIG.  393. — Connections  for  determining  form  factor. 

Determination  of  Form  Factor. — To  determine  the  form  factor, 
an  electrodynamometer  voltmeter  and  a  direct-current  voltmeter 
are  placed  in  parallel  as  shown  in  Fig.  393. 


DETERMINATION  OF  WAVE  FORM 


629 


The  direct-current  instrument  gives  the  mean  value  while  the 
electrodynamometer  gives  the  root-mean-square  value.  The 
deflections  are  controlled  by  non-reactive  resistances,  the  values 
of  which  need  not  be  known.  With  the  commutator  running 
and  the  brushes  adjusted  for  reversal  at  the  zero  point  of  the 
wave  by  the  method  just  given,  both  instruments  are  read. 
Call  the  dynamometer  reading  D,  and  the  galvanometer  reading 
G;  then 


Effective 


p.D;  _ 

Average 


With  the  commutator  stationary  a  direct-current  P.D.  is  now 
applied.     Then,  if  D'  and  G'  are  the  readings, 


and  the  form  factor  is 


P.D.  effective       DG' 


F    =  P.D.  average        D'G 

The  Oscillograph.5 — All  of  the  methods  for  obtaining  wave 
form  that  have  been  given  require  that  the  phenomena  be  periodic 
and  that  the  circuit  conditions  remain  fixed  for  a  considerable 
time.  Also  with  some  of  the  methods  much  time  must  be  spent 
in  calculating  and  plotting  the  results.  Cases  are  continually 
arising  where  it  is  desirable  to  investigate  phenomena  which  are 
transient  in  character,  as  for  example,  that  illustrated  in  Fig.  394. 


0.01  Second 

FIG.  394. — Showing  variation  of  current  and  voltage  during  short-circuit 
test  of  100-ampere  enclosed  fuse. 


630  ELECTRICAL  MEASUREMENTS 

Nominal  busbar  voltage 230  volts 

Minimum  busbar  voltage 61  volts 

Maximum  busbar  voltage 586  volts 

Maximum  current 6,600  amperes 

Time  required  to  open  circuit.. .  .  0.0086  second 

Time  required  to  attain  maxi- 
mum current 0 . 006  second 

Average  rate  of  decrease  of 

current 4,100,000  amperes  per  second. 

It  is  obvious  that  in  this  case  the  previous  methods  are  not 
applicable. 

Blondel  was  the  first  to  definitely  state  the  conditions  which 
must  be  fulfilled  in  order  that  a  galvanometer  may  follow,  with 
sufficient  accuracy,  the  rapid  variations  of  an  alternating  cur- 
rent and  be  capable  of  recording  wave  forms  photographically 
with  but  a  single  traverse  over  the  photographic  plate  of  the  spot  of 
light  which  is  used  as  an  indicator.  He  applied  the  term  oscillo- 
graph to  such  an  instrument. 

The  conditions  are  as  follows: 

1.  High  free  period  of  oscillation,  as  great  as  50  times  that  of 
the  phenomena  to  be  investigated. 

2.  Damping  small  and  in  the  neighborhood  of  the  critical 
aperiodic  value. 

3.  Self-induction  as  small  as  possible. 

4.  Negligible  hysteresis  and  Foucault  current  effects. 

5.  Adequate  sensitivity. 

In  addition,  the  design  and  construction  must  be  such  that  the 
necessary  adjustments  and  repairs  may  be  made  with  ease  by  any 
one  accustomed  to  handling  electrical  instruments. 

The  moving  needle,  the  moving  coil,  the  string  galvanometer, 
and  the  hot-wire  instrument  have  all  been  modified  so  that  they 
may  be  used  as  oscillographs.  BlondeFs  first  instrument  was  of 
the  moving-needle  type;  in  its  late  development  the  needle  has 
become  a  thin  strip  of  soft  iron  stretched  over  bridge  pieces,  as 
shown  in  Fig.  395. 

Referring  to  Fig.  395,  the  thin,  soft  iron  strip,  s,  is  drawn 
taut  over  the  bridge  pieces  by  the  spring  within  the  tube,  t.  The 
tension  is  controlled  by  the  nut  s.  The  strip  is  supported  and 
protected  by  an  insulating  tube,  T,  in  the  sides  of  which  soft  iron 


DETERMINATION  OF  WAVE  FORM 


631 


pole  pieces,  P,  are  inserted  so  that  the  middle  of  the  iron  strip  is 
in  a  very  narrow  air  gap.  Midway  between  the  bridge  pieces, 
and  behind  a  small  window,  the  minute  mirror,  m,  is  attached 
to  the  strip.  This  movable  system  fits  between  the  laminated 
poles  of  a  powerful  electromagnet  which  conforms  to  the  out- 
side of  the  tube.  The  middle  part  of  the  soft  iron  strip  thus 
becomes,  in  effect,  a  polarized  needle.  The  required  damping 
is  obtained  by  filling  the  tube  with  a  transparent  oil  of  the  proper 
viscosity. 


A-     A 


D 


FIG.  395. — Galvanometer  for  Blondel  moving-needle  oscillograph. 

The  current  whose  wave  form  is  to  be  determined  is  led  through 
two  coils  placed  with  their  common  axis  perpendicular  to  the 
magnetic  axis  of  the  needle.  On  the  passage  of  the  current,  the 
needle  will  deflect  like  that  of  an  ordinary  galvanometer  and  the 
spot  of  light  will  be  moved  across  the  photographic  surface. 

This  type  of  instrument  may  be  given  a  very  high  free  period 
of  vibration,  but  has  the  disadvantage  that  its  self-induction  is 
comparatively  large. 


632 


ELECTRICAL  MEASUREMENTS 


Blondel's  suggestion  for  making  the  moving-coil  galvanome- 
ter available  as  an  oscillograph  is  illustrated  in  Fig.  396. 

A  single  loop  of  a  narrow  and  very  thin  conducting  strip  is 
stretched  over  a  frame  in  such  a  manner  that  the  part  between 
the  bridge  pieces  a  and  b  is  free.  A  very  small  and  very  light 
mirror  is  cemented  to  the  two  sides  of  the  loop  midway  between 
the  bridges.  "The  loop  is  placed  between  the  poles  MS  of  a  power- 
ful electromagnet  which  is  worked  at  high  saturation.  The 
poles  are  large  enough  so  that  the  free  section  of  the  loop  is  in  a 
practically  uniform  field. 


FIG.  396. — Showing  principle  of  bifilar  oscillograph. 

A  current  passing  around  the  loop  will  cause  one  side  to  advance 
while  the  other  recedes;  the  mirror  is  thus  turned  around  a 
vertical  axis.  For  the  very  small  movements  which  are  employed, 
the  deflections  of  the  mirror  are  proportional  to  the  current. 

The  movable  system  is  immersed  in  oil  of  such  a  viscosity 
that,  at  the  normal  temperature  of  operation,  the  galvanometer 
is  dead  beat. 

The  material  from  which  the  strip  is  drawn  should  have  a  low 
resistivity  so  that  there  will  be  little  heating.  This  avoids 
creeping  of  the  spot  of  light  due  to  the  expansion  of  the  strip 
and  reduces  the  energy  consumed  by  the  galvanometer. 

This  form  of  instrument  has  the  advantage  that  the  inductance 
is  very  small  and  is  the  one  to  which  the  most  attention  has  been 
given  by  designers  in  the  United  States  and  in  England. 

Fig.  397  shows  a  group  of  oscillograph  vibrators.  The  corre- 
sponding galvanometers,  complete,  are  shown  in  Fig.  398. 

In  A,  which  is  intended  for  high-tension  work,  a  permanent 
magnet  is  used.  The  disadvantage  is  the  decreased  sensitivity. 
In  B  the  galvanometer  elements  are  thoroughly  insulated  from 


DETERMINATION  OF  WAVE  FORM 


633 


each  other,  so  that  it  is  not  necessary  that  the  vibrators  be  kept 
approximately  at  the  same  potential.  With  A,  the  potential 
difference  between  the  two  vibrators  and  also  that  between  the 
vibrators  and  the  frame  of  the  instrument  should  not  exceed 
50  volts. 

The  minimum  free  period  which  it  is  practicable  to  give  this 
form  of  vibrator  appears  to  be  about  Ko>ooo  second.     To  attain 


Tension  Adjustment 


FIG.  397. — Oscillograph  vibrators.     A,  Cambridge  Scientific  Instrument  Co. ; 
B,  General  Electric  Co. 

this  figure  the  parts,  especially  the  mirror,  must  be  exceedingly 
delicate;  this  increases  the  liability  to  accident  and  the  difficulty 
of  making  repairs. 

Instruments  with  such  a  high  rate  of  vibration  are  useful  and 
indeed  essential  in  certain  research  work,  but  they  must  be 
used  by  skilled  operators.  For  general  engineering  work  it  is 
better  to  be  content  with  a  more  robust  vibrator,  having  a  free 
period  of  about  J^,ooo  second.  Such  an  instrument  will  follow 
the  waves  usually  encountered,  closely  enough  for  practical 
purposes. 


634 


ELECTRICAL  MEASUREMENTS 


For  demonstration  purposes  oscillographs  are  made  which  are 
capable  of  projecting  the  curves  on  a  screen.  They  are  provided 
with  large  mirrors  and  have  a  free  period  of  from  M>500  to 


B 

FIG.  398. — Oscillograph  galvanometers.     A,  Cambridge   Scientific   Instru- 
ment Co.;  B,  General  Electric  Co. 

M >ooo  second.     Fig.  399  shows  such  an  instrument*  together  with 
the   auxiliary   apparatus.     It  is   provided   with   two   vibrators 
*  Designed  and  built  by  H.  G.  CRANE,  Brookline,  Mass. 


DETERMINATION  OF  WAVE  FORM 


635 


(period  about  ;K>500  second),  one  for  the  current,  the  other  for 
the  potential.  They  have  the  necessary  adjustments  for  properly 
locating  the  spots  of  light  on  the  screen.  No  damping  arrange- 
ment is  employed.  The  rotating  multisided  mirror  is  driven  by 
gearing  from  a  simple  synchronous  motor  which  is  easily  started 
by  giving  the  mirror  a  twist  just  as  the  switch  is  closed.  The 
arc,  which  is  enclosed,  can  be  readily  adjusted  as  to  position  and 
requires  little  attention.  Small  carbons  are  used  and  a  very 
intense  and  well-defined  spot  of  light  is  obtained. 


FIG.  399. — Demonstration  oscillograph. 

With  the  screen  at  a  distance  of  12  feet,  the  amplitude  of  the 
wave  is  about  2  feet,  while  the  length  of  the  wave  is  2^  feet. 
Both  the  shunt  and  the  multiplier  are  adjustable  so  that  the  am- 
plitude of  the  wave  may  be  varied. 

Naturally,  as  the  period  of  an  oscillograph  galvanometer  is 
very  short,  the  sensitivity  is  low.  In  the  laboratory  form  of 
instrument  a  deflection  on  the  scale  of  from  1  to  3  mm.  usually 
corresponds  to  about  0.01  ampere. 

The  movable  mirror  is  very  small  so  an  intense  source  of  light 
is  required.  A  direct-current  arc  is  commonly  employed.  The 
beam  of  light,  after  being  reflected  from  the  oscillograph  mirror, 


636  ELECTRICAL  MEASUREMENTS 

Fig.  400,  passes  through  a  long  cylindrical  lens  which  compresses 
the  beam  vertically.  This  focusing  improves  the  definition  of 
the  spot  of  light  on  the  screen  and  a  still  further  improvement  is 
effected  by  placing  a  narrow  vertical  slit  between  the  arc  and  the 
mirror. 

For  visual  observations  the  beam  of  light  after  passing  through 
the  cylindrical  lens  is  received  on  a  multisided  mirror  which  is 
rotated  at  the  proper  speed  by  a  synchronous  motor,  or  else  on 
a  mirror  which  is  tilted  with  a  uniform  angular  velocity  by  a  cam, 
also  driven  by  a  synchronous  motor.  With  the  tilting  mirror 
arrangement  a  shutter  actuated  by  the  motor  cuts  off  the  light 
while  the  cam  is  returning  the  mirror  to  its  initial  position. 


Cylindrical 

kens_/] }i \  Stationary 

i     Mirror 


©  J    Synchronous 
Mirror 


Total  Reflecting 
-—•=~r~-^ 

:=E£--- 


Arc 

FIG.  400. — Showing  optical  system  of  oscillograph. 

The  revolving  mirror  furnishes  the  necessary  time  coordinates. 
From  it  the  spot  of  light  is  reflected  upon  a  curved  translucent 
screen  which  is  concentric  with  the  axis  of  the  mirror. 

With  periodic  phenomena  the  waves  appear  in  a  fixed  position 
on  the  screen,  and  may  be  traced  on  thin  paper. 

For  photographic  work  these  mirror  arrangements  are  dis- 
pensed with  and  the  spot  of  light  is  focused  by  the  cylindrical 
lens  directly  on  a  photographic  surface  which  is  carried  either  by 
a  falling  plate  or  by  a  uniformly  rotating  drum.  With  the  drum 
a  shutter  is  employed  which  remains  open  while  the  drum  makes 
one  revolution.  The  mechanical  features  of  these  recording 
devices  are  described  in  the  catalogues  of  various  instrument 
makers. 

As  it  is  necessary  to  decrease  the  inertia  of  the  moving  parts 
of  the  oscillograph  vibrator  as  much  as  possible,  the  principle 


DETERMINATION  OF  WAVE  FORM 


637 


of  the  string  galvanometer  has  been  employed  by  some  designers, 
for  in  this  instrument  there  is  no  mirror  to  be  moved. 

In  Fig.  401  the  shell  and  pole  pieces  of  an  iron-clad  electro- 


10 


3-4 


I — 6 


3-4 

8  ^8       7 

FIG.  401. — Ganz  oscillograph,  a  modified  string  galvanometer. 

magnet  are  at  1  and  2.     The  exciting  coils  are  at  5.     The  strength 
of  field  in  the  air  gap  is  from  28,000  to  30,000  c.g.s.  units. 

The  moving  parts  or  " strings"  are  at  6.  Starting  from  the 
terminal  9  the  thin  metal  strip  which  serves  as  the  " string"  passes 
down  between  the  bridges  3  and  4, 
along  the  air  gap  to  3'  and  4',  around 
the  pulley  and  up  between  the  same 
set  of  bridges  to  the  terminal  10. 
Both  the  descending  and  the  ascend- 
ing parts  of  the  strip  are  thus  brought 
into  the  same  plane.  The  free  vibrat- 
ing length  of  the  strip  is  from  3  to  5 
cm.  The  necessary  tension  is  given 
by  the  spring  7  and  a  period  of  from 
34>ooo  to  K,ooo  second  is  obtained. 
At  8  is  a  third  terminal  which  is 
common  to  the  two  parts  of  the-  strip, 
one  of  which  is  used  for  the  current,  the  other  for  the  potential 
vibrator,  as  is  indicated  in  Fig.  402. 

A  hole  is  bored  axially  through  the  pole  pieces  so  that  by  means 


D.C. 


FIG.    402. — Arrangement    of 
circuits  in  Ganz  oscillograph. 


638  ELECTRICAL  MEASUREMENTS 

of  a  projecting  microscope  the  images  of  the  strips  may  be  thrown 
either  on  a  uniformly  moving  photographic  surface,  for  the  pur- 
pose of  obtaining  a  permanent  record,  or  on  a  translucent  screen 
for  visual  observations. 

When  permanent  records  are  taken,  the  photographic  surface 
is  caused  to  move  in  a  direction  parallel  to  the  length  of  the  strips, 
and  immediately  behind  a  narrow  transverse  slit.  The  projec- 
tions of  the  strips  cross  the  slit  and  on  the  passage  of  the  alternat- 
ing current  move  back  and  forth  along  it.  The  photographic 
trace  is,  therefore,  a  light  line  on  a  dark  ground. 

For  visual  observations  the  image  of  the  strips  is  focussed  on  a 
small  ground-glass  screen,  immediately  behind  which  is  placed  a 
strbboscopic  disc  with  narrow  radial  slits.  If  the  disc  be  station- 
ary there  will  be  a  bright  vertical  line  of  light  on  the  screen,  cross- 
ing which  is  the  dark  projection  of  the  strips.  The  position  of 
this  depends  on  the  current  strength;  when  the  disc  is  rotated,  a 
series  of  flashes  sweep  across  the  screen  and  as  the  rotation  is 
synchronous  with  the  current,  the  curves  appear  stationary  on 
the  screen. 

Theory  of  the  Oscillograph.  —  As  the  oscillograph  is  merely  a 
damped  galvanometer  with  a  high  free  rate  of  vibration,  the 
equation  established  on  page  25  applies.  As  the  current,  and  con- 
sequently the  deflecting  force,  may  be  any  function  of  the  time, 
it  must  be  expressed  analytically  by  a  Fourier  series.  Conse- 
quently 


t  =       n  sn 

co  is  2?r  times  the  fundamental  frequency  of  the  current  and  n  is 
the  order  of  any  harmonic.  For  the  fundamental  n  is  1,  for 
the  third  harmonic  n  is  3,  and  so  on. 

If  the  second  member  of  1  is  zero,  and  the  relative  values  of 
P,  k  and  r  are  such  that  the  motion  is  oscillatory, 

(2) 

K  and  <p  are  .constants  which  are  determined  by  the  initial 
conditions.  X  is  the  logarithmic  decrement  and  T  is  the  time  of 
a  complete  vibration  (see  page  29). 

On  account  of  the  damping  the  transient  portion  of  the  deflec- 


DETERMINATION  OF  WAVE  FORM  639 

tion,  represented    by  6',  rapidly  diminishes  to  zero  after  the 
circuit  is  closed. 

The  particular  integral  to  which  Bf  must  be  added  to  obtain 
the  complete  integral  is 

6  =  C  Vn        —7=  =  sin  (nut  —  (3n  — 

Wu2  +  (r  -  n2co2P)2          \ 


This  expression  for  6  should  be  compared  with  the  corresponding 
one  for  the  flow  of  current  in  a  circuit  containing  resistance, 
inductance  and  capacity  after  the  steady  state  has  been  estab- 
lished. In  both  cases  there  are  "  impedance"  and  phase-cjis- 
placement  terms. 

Inspection  of  (3)  shows  that  after  the  transient  term  has 
disappeared, 

1.  The  various  harmonics  do  not  have  the  same  proportional 
effect  on  the  deflection. 

2.  The  harmonics  suffer  different  phase  displacements. 

In  consequence,  the  oscillograph  can  never  give  a  mathematic- 
ally correct  picture  of  a  wave  form.  This  being  so,  it  is  neces- 
sary to  find  the  conditions  which  will  make  the  instrument 
sufficiently  correct  for  practical  purposes. 

Obviously,  if  the  moment  of  inertia  and  the  damping  were  both 
zero  the  wave  would  be  followed  exactly.  Therefore,  the  mass 
of  the  moving  parts  must  be  reduced  to  a  minimum  and  an  ar- 
rangement adopted  which  will  make  the  moment  of  inertia  as 
small  as  possible.  At  the  same  time  the  directive  moment  on 

J2/3 

the  movable  system  must  be  increased  so  that  the   -,  2~  and  the 

-JT  terms  are  small  in  comparison  with  it;  hence  the  usual  state- 

ment that  the  rate  of  free  vibration  must  be  high. 

The  instrument  must  closely  follow  sudden  changes  of  cur- 
rent, therefore,  the  damping  should  be  near  the  critical  value, 
or  mathematically, 

k2  =  4rP. 
Then 


640  ELECTRICAL  MEASUREMENTS 

Consequently,  with  the  critically  damped  oscillograph,  the  ratio 
of  the  amplitude  of  the  deflection  due  to  a  given  harmonic  to  the 
value  it  would  have  if  the  instrument  were  perfect,  that  is,  with- 
out inertia  and  without  damping,  is  given  by 

_r 1 

1    +   U^  47T* 

IP 

The  free  period  of  the  movable  system  is  T0  =  2w  */—  and  if 
the  periodic  time  of  the  phenomena  under  investigation  is  T7, 

r> 

(5) 


or 


To        1    /I 
T     ~  n\R, 


1  (6) 


Suppose  the  natural  period  of  the  movable  system  is  %,ooo 
second  and  that  60-cycle  phenomena  are  being  investigated. 
Then  for  the  fundamental  and  the  ninth  and  the  twenty-first 
harmonics, 

~     =  a9999 


0-"2 


1  +  0.0081 
#21  =  0.956 

These  departures  from  exact  proportionality  are  negligible  in 
almost  all  cases. 

As  another  example,  suppose  that  it  is  desired  to  reproduce 
the  fifth  harmonic  to  within  1  per  cent.  Then 

R,  =  0.99 


~  =  ^u)         =  0.02. 

That  is,  for  the  assigned  degree  of  accuracy  the  frequency  of 
the  vibrator  should  be  50  times  that  of  the  phenomena  under 
investigation,  or  the  rate  of  the  vibrator  should  be  3,000  per 
second  when  dealing  with  the  fifth  harmonic  in  a  60-cycle  circuit. 


DETERMINATION  OF  WAVE  FORM  641 

The  phase  displacement  of  any  particular  harmonic  is  given  by 

knu  2n 


If  No  and  N  represent  the  number  of   vibrations  per  second, 
corresponding  to  To  and  T  respectively, 

2n^ 
tan  0'n  =  -^vr-^-^  =    ,.T^N   -.  (8) 


-N-   IN,     \JT) 

If  *  _  ^00  _  100>  ^ 

200 
tan  0'i    =  1Q  000  _  l  =  0.020  o  1°.15  of  the  fundamental 

1  800 
tan  /3'9    =  in     ' ^T  =  0.182  o  10°.3  of  the  ninth  harmonic 

1U,UUU  —  ol 

tan  j3'2i  =  0.439  =c=  23°.7    of   the   twenty-first 

harmonic. 

If  the  length  of  one  complete  cycle  of  the  curve  is  2.5  in.,  the 
corresponding  linear  displacements  are 

for  0'i 0.0080  in. 

for  j8'9 0.0079  in. 

for  ft' 21 0.0078  in. 

It  will  be  noted  that  all  the  components  are  shifted  from 
the  positions  they  would  occupy  with  a  perfect  instrument  by 
practically  the  same  amount,  so  that  no  error  of  importance  is 
introduced  by  the  phase  displacements. 

The  Electrostatic  Oscillograph.6 — The  electrostatic  oscillo- 
graph is  a  form  of  electrometer  so  designed  that  the  rate  of 
free  vibration  is  high  and  the  damping  of  proper  value.  The 
instrument  is  used  heterostatically.  The  high  free  period 
necessitates  a  strong  controlling  force,  and  this,  together  with 
the  fact  that  electrostatic  forces  are  small  when  low  potentials 
are  concerned,  means  that  the  electrostatic  oscillograph  is  natu- 
rally best  adapted  to  high-voltage  work.  For  such  work  it 
possesses  the  advantage  that  it  consumes  no  energy  and  that  the 
current  required  is  exceedingly  small,  being  only  that  necessary 

41 


642 


ELECTRICAL  MEASUREMENTS 


to  charge  it  and  to  charge  the  condenser  multipliers  which  are 
used  at  very  high  voltages. 

In  the  instrument  devised  by  Ho  and  Koto,  Fig.  403,  the  poten- 
tial to  be  measured  is  applied  between  the  plates,  FI  and  F2, 

either  directly,  or  through  a  con- 
denser multiplier  if  the  voltages  are 
very  high.  These  plates  serve  as 
"  quadrants."  They  are  9  mm. 
wide  and  15  mm.  long,  are  exactly 
alike  and  placed  5  mm.  apart.  The 
mirror  m  is  observed  through  one 
of  the  openings,  wi,  the  other  open- 
ing, Wz,  being  added  in  order  that 
the  arrangement  may  be  sym- 
metrical. 

The  condensers,  Ci  and  C2,  serve 
to  split  the  potential  which  is  ap- 
plied between  the  " quadrants." 
They  are  nominally  of  the  same 
capacity;  one  of  them  must  be 
adjustable.  The  condenser  multi- 
plier is  introduced  by  the  inser- 
tion of  the  condenser,  C. 
The  moving  members,  or  "  needles,"  are  formed  by  two  metal 
strips,  81  and  s2.  As  in  the  ordinary  oscillograph  they  are 
stretched  by  a  spring,  q,  between  insulating  bridge  pieces.  They 
are  insulated  from  each  other  at  their  lower  ends  by  the  silk 
thread  gph.  The  " needles"  are  charged  from  a  300-volt  battery 


FIG.  403.— Diagram  of  elec- 
trostatic oscillograph,  of  Ho  and 
Koto. 


FIG.    404. — Pertaining  to  demonstration  for  electrostatic  oscillograph. 

of  dry  cells,  B.     The  middle  of  the  battery  is  connected  to  the 
point  d,  between  the  condensers  Ci  and  C2. 

Suppose  the  electrometers  to  be  perfectly  symmetrical;  the 
arrangement  is  that  shown  in  Fig.  404.  Consider  a  fall  of  poten- 
tial to  be  positive  in  the  direction  of  the  arrow.  Let  e  be 


DETERMINATION  OF  WAVE  FORM  643 

the  voltage  between  Fi  and  F2  at  any  instant  and  let  B  be  the 
constant  e.m.f.  of  the  well  -insulated  battery.  FI,  F2  and  Si 
may  be  regarded  as  forming  the  elements  of  one  electrometer 
and  Fi,  F2  and  s2,  those  of  another.  The  two  moving  elements 
or  needles  are  mechanically  coupled  by  the  mirror,  m,  which  is 
cemented  to  both. 

It  has  been  shown  (see  page  250)  that  the  force  acting  on  the 
movable  element  of  an  electrometer  may  be  represented  by 

/  =  K(2Vd  +  d2) 

where  d  is  the  fall  (or  rise)  of  potential  from  quadrant  1  to  quad- 
rant 2  and  V  is  the  fall  (or  rise)  of  potential  from  quadrant  2 
to  the  needle.  Applying  this  to  the  case  in  hand,  for  the  electro- 
meter Fi,  F2  and  si, 


!  ==  K\2e  (-  I  +     )  +  e2]  =  +KBe 


KBe. 


and  for  the  electrometer  FI,  F2,  s2, 

/,  =  «[&(-  I  -  f)  +  «']  =  -K 

Therefore,  the  mirror  which  is  cemented  between  Si  and  s2  is 
acted  upon  by  a  couple  proportional  to  Be.  If  the  natural  period 
of  the  instrument  be  high  (a  frequency  of  3,500  vibrations  per 
second  may  be  obtained),  and  if  proper  damping  is  employed, 
the  deflection  at  every  instant  is  6  =  kBe,  that  is,  the  instrument 
follows  the  wave  as  does  an  ordinary  oscillograph. 

Obviously  it  is  necessary  to  prevent  sparking  between  the 
various  parts  of  the  instrument  and  across  the  condensers. 
Consequently  the  entire  system,  FI,  si,  s2,  F2,  is  immersed  in  a 
transparent  oil  of  high  dielectric  strength  and  the  condensers 
are  similarly  treated.  It  is  essential  that  no  dielectric  losses 
occur,  as  they  would  introduce  phase  displacements. 

Adjustment  of  Electrostatic  Oscillograph.  —  If  the  voltage  B 
is  zero,  the  instrument  should  experience  no  deflection;  it  is, 
however,  practically  impossible  to  construct  the  instrument  with 
the  mathematical  accuracy  assumed  above,  so  the  following 
adjustment  is  necessary. 

Make  B  equal  to  zero,  that  is,  connect  both  strips  to  d  and 
apply  the  full  alternating  voltage  between  FI  and  Fa.  In  general, 


644  ELECTRICAL  MEASUREMENTS 

the  strips  will  vibrate  with  a  frequency  twice  that  of  the  voltage. 
One  of  the  condensers,  Ci,  C2,  is  then  adjusted  until  this  deflec- 
tion disappears.  If  the  adjustment  is  not  perfect,  the  two  halves 
of  a  symmetrical  alternating-current  wave  will  appear  dissimilar. 
If  the  connection  at  k  is  not  at  the  correct  point,  the  wave  will 
be  shifted  with  respect  to  the  zero  line. 

The  metallic  vibrator  case  should  be  connected  to  d.     The 
sensitivity  can  be  varied  by  altering  B. 


|VWv4wWS p — - 


FIG.  405. — Connections  for  determining  the  wave  form  of  a  small  current 
by  electrostatic  oscillograph. 

The  sensitivity  attained  is  as  follows:  with  B  =  300  volts, 
e  =  2,000  volts,  effective,  scale  distance  70  cm.,  the  amplitude 
of  wave  trace  is  2  cm. 

For  the  measurement  of  very  small  currents  the  connections 
shown  in  Fig.  405  may  be  used.  The  voltage  B  is  made  very 
large  by  using  either  a  high-tension  battery  or  two  condensers 
in  series  which  are  continuously  charged  from  an  influence 
machine. 

s 

T     ft 


FIG.  406. — Braun  tube  for  determining  wave  form. 

The  Braun  Tube. — The  Braun  tube7  is  a  form  of  vacuum  tube 
especially  designed  for  determining  wave  form. 

Fig.  406  gives  an  idea  of  the  tube  as  now  made.  The  alu- 
minum cathode  is  at  K,  the  anode  at  A ;  they  should  not  be  less 
than  15  cm.  apart.  At  T7  is  a  grounded  brass  target,  pierced 
by  a  small  hole  about  0.5  mm.  in  diameter.  The  glass  screen, 
S,  is  covered  with  zinc  sulphide,  or  calcium  tungstate. 


DETERMINATION  OF  WAVE  FORM 


645 


To  obtain  a  uniform  sensitivity  and  a  sharply  defined  spot 
where  the  cathode  rays  impinge  upon  the  screen,  it  is  essential 
that  a  constant  exciting  voltage  be  used,  from  10,000  to  20,000 
volts  being  required,  unless  the  cathode  is  heated. 

The  cathode  rays  proceed  perpendicularly  outward  from  the 
electrode,  K,  and  fall  on  the  target,  T,  where  most  of  them  are 
stopped.  A  small  pencil  of  rays,  however,  passes  through  the 
opening  and  falls  on  the  screen,  S,  producing  a  bluish  fluorescent 
spot.  Just  in  front  of  the  target  are  placed  two  deflecting  coils 


+  30 

/ 

+  20 

a 

3 
t) 

/ 

/ 

+10 

I 

/ 

. 

/ 

/ 

-1 

X)  -8 

o  -e 

0   -4 

B    -2 

/ 

7 

-10 

42 
A 

)    +4 

oiper 

9    +( 

es 

0   +8 

0   +1 

X) 

/ 

/ 

/ 

-20 

/ 

/ 

-30 

> 

FIG.  407. — Showing  proportionality  of  deflection  and  current  with  a  Braun 

tube. 

with  their  common  axis  transverse  to  that  of  the  tube.  The 
magnetic  field  set  up  by  these  coils,  when  traversed  by  a  current, 
deflects  the  cathode  stream  and  Fig.  407  illustrates  the  relation 
between  the  deflection  of  the  fluorescent  spot  and  the  current. 
It  is  seen  that  the  deflection  is  proportional  to  the  current  and 
that  it  reverses  when  the  current  is  reversed. 

When  an  alternating  current  is  passed  through  the  deflecting 
coils,  the  spot  stretches  out  into  what  appears  to  be  a  fluores- 
cent band.  If  this  band  is  viewed  in  a  revolving  mirror  the 


646  ELECTRICAL  MEASUREMENTS 

wave  form  appears.  This  is  the  common  arrangement  for 
visual  observations. 

As  the  cathode  stream  is  without  inertia,  the  deflection  will 
follow  waves  of  the  highest  frequency  without  error.*  In  this 
the  Braun  tube  is  unique  among  devices  for  tracing  wave  forms. 

As  the  cathode  stream  is  deflected  as  readily  in  one  direction 
as  in  another,  the  spot  of  light  will  take  up  a  position  dependent 
not  only  on  the  magnitude  but  on  the  direction  of  the  resultant 
field  due  to  any  system  of  magnetizing  coils.  This  is  a  second 
unique  feature  of  the  instrument. 

Permanent  Records  by  Braun  Tubes. — To  obtain  a  permanent 
record  it  is  necessary  to  introduce  a  time  coordinate  in  some 
manner.  The  simplest  method  is  to  photograph  the  fluorescent 
spot  on  a  film  carried  by  a  synchronously  rotating  drum ;  the  wave 


FIG.  408. — Showing  oscillatory  current  due  to  the  discharge  of  a  condenser 
through  an  inductive  resistance.     Taken  with  Braun  tube. 

then  appears  on  the  film  in  rectangular  coordinates.  The  curve 
shown  in  Fig.  408  was  taken  in  this  manner.  As  the  photo- 
graphic intensity  of  the  fluorescent  spot  is  not  great,  the  Braun 
tube  is  adapted  to  recording  periodic  phenomena  only.  To  ob- 
tain the  curve  shown  in  Fig.  408  the  circuit  was  made  and 
broken  by  a  commutator  attached  to  the  axle  of  the  drum  and  the 
spot  of  light  traversed  the  same  path  on  the  film  many  hundred 
times.  The  inability  to  obtain  records  by  a  single  traverse  of 
the  image  of  the  spot  over  the  photographic  surface  is  a  serious 
drawback  to  this  form  of  oscillograph.  Another  limitation  is 
apparent  from  the  figure.  The  width  of  the  line  which  is  traced 
is  considerable  when  compared  with  the  amplitude  of  the  curve. 

*  See  paper  by  DR.  E.  L.  CHAFFEE,  Proc.  American  Academy  of  Arts 
and  Sciences,  vol.  ,47,  1911-12,  p.  267. 


DETERMINATION  OF  WAVE  FORM 


647 


Another  disadvantage  is  that  there  is  necessarily  considerable 
inductance  in  the  deflecting  coils. 

A  second  method  of  introducing  the  time  coordinate  is  to  use 
two  sets  of  deflecting  coils  with  their  axes  at  right  angles  to  each 
other  and  perpendicular  to  the  axis  of  the  tube.  One  set  of  coils 
is  traversed  by  the  current  whose  wave  form  is  desired,  the  other 
by  a  current  of  a  simple  and  known 
wave  form.  This  auxiliary  current 
must  vary  synchronously  with  the  un- 
known current,  and  it  may  have  a 
linear  wave  form,  the  current  strength 
increasing  uniformly  with  the  time,  or 
it  may  have  a  sinusoidal  form. 

Zenneck7  uses  the  linear  wave, 
which  he  obtains  by  the  synchron- 
ously rotated  slide-wire  arrangement 
sketched  in  Fig.  409.  The  effect  is 
to  cause  the  fluorescent  spot  to 
progress  regularly  across  the  screen 
with  every  revolution  of  the  slide 
wire.  At  the  same  time  the  regular 

deflecting  coils  cause  the  spot  to  be  deflected  in  a  perpendicular 
direction.  The  result  is  that  the  curve  appears  to  stand  still  on 
the  screen.  It  can  be  photographed  by  an  ordinary  camera  or 
traced  on  a  suitable  transparent  screen,  the  eye  being  kept  in 
a  fixed  position.  Perfect  action  of  the  brushes  is,  of  course, 
essential. 


To  Coils 


FIG.  409. — Diagram  of 
rotary  slide  wire  for  use  with 
Braun  tube  to  introduce  the 
time  coordinate. 


FIG.  410. — Electrostatic  tube  for  determining  wave  form. 

Electrostatic  Tubes. — The  cathode  rays  may  also  be  deflected 
electrostatically.  To  this  end  two  condenser  plates  are  mounted 
so  that  the  cathode  stream  passes  between  them,  the  plates  being 
either  inside  or  outside  the  tube.  The  deflection  is  proportional 
to  the  potential  difference  between  the  plates  and  may  be  ad  justed 
by  varying  their  distance  apart.  For  very  high  voltages  a  con- 
denser multiplier  must  be  used.  Ryan  and  Minton  have  em- 


648  ELECTRICAL  MEASUREMENTS 

ployed  this  principle  in  the  electrostatic  power  indicator,  or 
cyclograph,  see  page  326. 

General  Considerations. — In  order  that  the  tube  may  oper- 
ate satisfactorily  it  is  essential  that  the  vacuum  be  properly 
adjusted.  As  the  degree  of  vacuum  changes  with  use  of 
the  tube,  (usually  increasing  with  the  time),  some  experi- 
menters, in  work  of  long  duration,  keep  the  tube  attached  to  the 
air  pump  so  that  the  vacuum  may  be  adjusted  at  will,  while  others 
have  used  different  forms  of  vacuum  regulator.  One  such  device 
consists  of  a  thin  platinum  or  palladium  tube,  closed  at  the  outer 
end  and  sealed  into  the  vacuum  tube.  If  the  vacuum  be  too  high, 
the  outer  end  of  the  platinum  tube  is  heated  for  an  instant  to  a 
dull  red  by  a  spirit  lamp ;  a  small  amount  of  hydrogen  will  then 
pass  into  the  tube  and  lower  the  vacuum.  This  arrangement 
gives  no  means  of  increasing  the  vacuum,  which  is  sometimes 
necessary. 

Trouble  may  be  caused  by  sparking  from  the  cathode  to  the 
glass  in  its  immediate  vicinity.  Such  sparking  should  be  avoided 
since  it  causes  the  cathode  ray  stream  to  be  unsteady.  The  glass 
becomes  positively  charged,  and  when  the  P.D.  between  the 
glass  and  the  cathode  becomes  high  enough  a  discharge  occurs. 

These  two  difficulties  are  serious  and  in  the  past  have  been 
sufficient  to  prevent  the  cathode  ray  tube  becoming  a  reliable 
and  convenient  instrument,  in  spite  of  the  fact  that  it  is  peculiarly 
adapted  to  certain  kinds  of  work. 

These  difficulties  have  to  do  with  the  film  of  gas  which  adheres 
to  the  surfaces  within  the  tube.  It  has  been  found  that  if  the 
tube  is  exhausted  at  a  temperature  of  about  350°C.,  and  the  time 
of  exhaustion  is  properly  adjusted,  about  one-half  hour,  a 
sufficient  quantity  of  the  adsorbed  gas  may  be  removed  so 
that  the  vacuum  will  remain  constant  during  long  periods  and 
still  leave  a  sufficient  film  on  the  glass  so  that  the  charges  on  it 
are  conducted  to  the  cathode  and  neutralized. 

Disturbing  effects  due  to  stray  electromagnetic  and  electro- 
static fields  must  be  eliminated,  the  latter  by  the  use  of  proper 
screens. 

Electrostatic  tubes  with  external  condenser  plates  should  be 
rendered  non-hygroscopic  in  the  neighborhood  of  the  plates  so 
that  the  moisture  may  not  screen  the  cathode  ray  stream. 


DETERMINATION  OF  WAVE  FORM  649 

Cellulose  nitrate  made  into  a  paste  with  ether  and  painted  on 
the  tube  for  a  distance  of  a  few  inches  on  each  side  of  the  plates 
effectively  prevents  this  trouble. 

Soft  sodium  glass  is  tl^e  best  material  for  the  tubes  as  it  is 
easily  worked  and  gives  the  least  trouble  from  electrostatic  effects. 
Also,  the  proper  time  during  which  the  tube  must  be  exhausted 
is  more  readily  adjusted  than  with  other  kinds  of  glass. 

The  tube  may  be  excited  by  a  motor-driven  electrostatic  ma- 
chine but  this  becomes  unreliable  in  damp  weather.  In  specially 
equipped  laboratories  a  storage  bat- 
tery of  small  cells,  capable  of  giving 
a  potential  of  20,000  volts,  has  been 
used.  A  synchronous  commutator, 
Fig.  411,  has  proved  very  service- 
able; by  it  the  peaks  of  the  waves  in 
the  secondary  of  the  small  high- 
tension  transformer  T  are  rectified 
and  applied  to  the  condenser,  C,  of 
Leyden  jars  in  parallel,  around  which  FIG.  411. — Diagram  of 

the  tube  is  shunted.  Good  contacts  synchronous  commutator 
.  ,  ,  method  of  exciting  Braun 

between  the  brushes  and  the   com-      tube. 

mutators    are    essential.       A    high- 
resistance  rod,  r,  of  about  100,000  ohms  is  connected  in  series 
and  directly  to  the  cathode  to  prevent  flash-over  and  to  cause 
the  tube  to  operate  more  steadily. 

The  intensity  of  the  spot  may  be  increased  by  using  a  focusing 
coil  traversed  by  direct  current.  The  coil  is  placed  axially  over 
the  tube  between  the  anode  and  the  cathode.  By  this  coil  the 
sensitiveness  of  the  tube  may  be  varied  somewhat,  and  the  vol- 
tage necessary  for  the  operation  of  the  tube  is  reduced.  Care- 
ful regulation  of  the  direct  current  is  necessary. 

When  working  with  high-frequency  currents  there  will  be,  on 
account  of  the  inductance,  large  differences  of  potential  between 
different  parts  of  the  deflecting  coils  and  a  large  electrostatic 
deflection  of  the  spot  may  occur.  This  may  be  eliminated  by 
surrounding  the  tube,  inside  the  deflecting  coils,  by  a  split 
solenoid  of  fine  insulated  wire  wound  on  a  paper  tube.  This 
forms  an  effective  electrostatic  shield  and  has  no  influence  on 
the  electromagnetic  deflection. 


650  ELECTRICAL  MEASUREMENTS 

WAVE  ANALYSIS 

Curves  taken  by  the  foregoing  methods  show  that  in  practice 
both  the  potential  difference  and  the  current  waves  may  depart 
widely  from  the  sinusoidal  form.  In  any  particular  case  after 
having  obtained  the  graph  of  the  wave,  it  is  possible  to  write 
its  equation  as  the  sum  of  a  series  of  sinusoidal  terms  of  multiple 
frequencies  which  have  the  proper  time-phase  relations. 

To  effect  such  an  harmonic  analysis,  recourse  is  had  to  the 
work  of  Fourier  who,  in  1812,  first  explicitly  showed  that  a 
function  which  is  subject  to  certain  mathematical  conditions 
can  be  represented  by  a  constant  term  plus  the  sum  of  a  sine 
and  a  cosine  series.8  This  result  he  published  in  his  "Theorie 
Analytique  de.  Chaleur,"  1822. 
Accordingly 

/(0)  =  Ai  sin  0  +  A  2  sin  20  +  A  3  sin  30  -f  . .    . 

+  -^  +  Bi  cos  0 .+  #2  cos  20  +  #3  cos  30  +  . 


(9) 


The  coefficients  are  given  by  the  following  equations:8 

Ak  =  i  f/(0)  sin  kOdO  (10) 

^Jo 

i  r2* 

Bk  =  -\  f(6)  cos  k8dO  (11) 


The  expression  (9)  is  called  a  Fourier  series. 

The  sine  and  cosine  terms  may  be  combined,  for 

A  sin  0  +  B  cos  0  =  \A2  +  £2  sin  (0  +  tan-1^)  =  Csin(0+a'). 

This  gives 

/W  =  ^  +  Ci  sin  (0  +  «',)  +  C2  sin  (20  +  a',)  + 

C3  sin  (30  +  a'8)  +  .    .    .      (12) 

If  the  origin  is  taken  at  the  zero  of  the  fundamental,  which 
is  convenient  if  the  waves  are  to  be  plotted, 

f(0)  =  ^  +  Ci  sin  0  +  C2  sin  2(0  +  <*2)  + 

C3  sin  3(0  +  a3)V  -    -    ,      (12o) 
where 


0/2  OL'?, 

T  :•*>  ^-1  -«>;etc- 


DETERMINATION  OF  WAVE  FORM 


651 


Here  an  is  measured  on  the  same  scale  as  6  and  the  zero  point 
of  any  component  is  where  it  first  passes  from  a  negative  to  a 
positive  value.  A  positive  value  of  an  indicates  a  leading  com- 
ponent. The  constant  .term  is  usually  absent  in  alternating- 
current  waves. 

The  effect  of  the  odd  and  even  harmonics  and  of  their  phase 
displacements  is  illustrated  in  Fig.  412.  Odd  harmonics  produce 
a  wave  the  second  half  of  which  is  like  the  first  with  the  algebraic 
signs  of  all  the  ordinates  reversed.  Even  harmonics  produce 
an  asymmetrical  wave. 


Old  Harmonics  Even  Harmonics 

FIG.  412. — Illustrating  the  effects  of  odd  and  of  even  harmonics. 

The  integrals  in  (10)  and  (11)  are  proportional  to  the  areas 
under  the  curves  which  would  be  obtained  if  each  value  of 
f(0)  were  multiplied  by  the  corresponding  value  of  sin  kd  or 
cos  kd  and  new  curves  plotted  on  the  same  base,  27r. 

Therefore, 

Ak  =  twice  the  average  ordinate  of  curve  /(0)  sin  kd          (10a) 
Bk  =»  twice  the  average  ordinate  of  curve  /(0)  cos  kd  (Ho) 

The  integration  could  be  performed  by  a  planimeter. 

The  labor  involved  in  carrying  out  the  process  just  indicated 


652  ELECTRICAL  MEASUREMENTS 

is  prohibitive,  but  machines  called  harmonic  analyzers  have  been 
devised,  some  of  which  practically  effect  the  determination  of 
A k  and  Bk  in  this  manner. 

The  various  coefficients  may  be  determined  arithmetically  as 
follows:  A  complete  cycle  of  the  curve  to  be  analyzed  is  plotted. 
The  base,  (2?r),  is  then  divided  into  2n  equal  spaces,  and 
ordinates  erected.  Let  the  measured  values  of  the  2n  ordinates 
be  2/0,  2/i  ?  2/2,  ...  2/2n-i-  The  distance  between  consecutive 

2ir       TT 

ordinates  is  A0  =  =-  =  -• 
2n      n 

By  (10a), 

2 

Ak  =  —  [2/0  sin  0  fcA0  -+•  2/1  sin  1&A0  -f-  2/2  sin  2&A0  +  .    .    .  + 

2/2n-2  sin  (2n  -  2)  /cA0  +  2/2«-i  sin  (2n  -  1)  /cA0]     (13) 

If  the  data  are  furnished  by  the  contact  method,  the  measure- 
ments being  made  at  equal  intervals  along  the  wave,  the  values 
of  2/o,  2/ij  etc.,  are  given  directly  and  the  curve  need  not  be  plotted. 
Equation  (13)  may  be  written 

1  ^2n~l 
Ak  =  -  ^          ym  sin  kmM  (14) 

where  m  is  the  number  of  the  ordinate  concerned  in  the  multiplica- 
tion; similarly 

Bk  =  ~  [2/0  cos  Okdd  +  2/1  cos  &A0  -f-  2/2  cos  2&A0  +  .    .    .  + 

71 

2/2n_2  cos  (2n  -  2)/cA0  +  y2n-i  cos  (2n  -  1)  &A0]     (15) 
ym  cos  kmAO  (16) 

Runge  Method  of  Grouping  Terms. — Theoretically  it  is  easy 
to  calculate  the  coefficients.  The  practical  difficulty  lies  in  the 
great  expenditure  of  time  which  is  necessary  for  carrying  out 
the  process  as  indicated.  For  this  reason  Runge9  has  intro- 
duced an  abridged  method  of  calculation  which  is  carried  out  by 
aid  of  a  systematically  arranged  schedule. 

In  the  majority  of  cases,  the  two  halves  of  an  alternating-cur- 
rent wave  are  the  same  except  for  the  algebraic  sign;  that  is, 


DETERMINATION  OF  WAVE  FORM  653 

only  the  odd  harmonics  are  present,  and  consequently  the  values 
of  k  are  odd  numbers.  It  is  necessary,  therefore,  to  deal  with 
only  one-half  of  the  wave,  and  2n  spaces  per  half  wave  are  used, 

making  A0  =  -^- 

The  method  of  grouping  the  terms  so  as  to  economize  time 
may  be  explained  as  follows.     Referring  to  (13),  y\  is  multiplied 

by  sin  g-  and  yzn-i  by  sin  (2n  —  l)^-     As  k  is  odd, 

.     kir          .     /,  kir\  kir 

sin  j—  =  sml  KIT  —  x-  I  =  sin  (2n  —  1)  =- 

2n  \  2ft/  '  2n 

and  in  general, 

N  /CTT         .      mkir 
sin  (2n  -  m)  ^  =  sin  -^-  (17) 

Consequently, 

1.  The  number  of  multiplications  may  be  halved  by  adding, 
before  taking  the  products,  those  values  of  y  for  which  the  sum  of 
the  subscripts  is  2n. 

2.  Again,  the   same   products   are  needed  in  Ak  and  A2n-k', 
that  is,  in  those  coefficients  for  which  the  sum  of  the  subscripts 
is  2n,  since 

±  sin  (2n  -  *)  £J  =  sin  k  ~  (18) 

If  the  number  of  the  ordinate  concerned  in  the  multiplication 
(m)  is  even,  the  sign  of  the  left  hand  member  is  — ,  and  if  m  is 
odd  the  sign  is  +. 

For  example,  suppose  a  half  period  is  divided  into  2n  =   12 

equal  parts  (A0  =  ^-  o  15°  j  and  the  ordinates  measured; 
then  by  (13)  and  (17) 

A  i  =  I/Q  [(yi  +  2/n)  sin  15°  +  (y,  +  y10)  sin  30°  + 
(2/8  +  2/9)  sin  45°  +  (y,  +  y*)  sin  60°  +  (y,  +  y-j)  sin  75°  +  2/6sin90°] 
Au=%  [(yi  +  yn)  sin  165°  +  (j/2  +  2/10)  sin  330°  + 
(l/s  +  2/9)  sin  495°  +  (y4  +  Vs)  sin  660°  +  (y6  +  j/7)  sin  825°  + 
i/6  sin  990°]. 

For  convenience  the  sines  of  all  the  angles  may  be  expressed 
in  terms  of  the  sines  of  angles  of  90°  or  less. 


654  ELECTRICAL  MEASUREMENTS 

Accordingly,  by  the  aid  of  (18)  the  value  for  An  may  be 
written, 

An  =  %  [(2/1  +  2/n)  sin  15°    -  (2/2  +  2/10)  sin  30°  +  (y3  +  2/9)  sin 
45°    -  (2/4  +  2/8)  sin  60°  +  (2/5  +  y7)  sin  75°  -  j/6  sin  90°]. 

Applying  the  rules, 

^3    =  %  [{(2/1  +   2/n)   +   (1/3  +  2/9)   --   (2/5  +  2/7)}  sin  45°  + 

!(2/2  +  2/io)  -  2/6 !  sin  90°] 
^9    =  H  [{(2/i  +  2/n)   +   (2/3  +  2/9)    -  -    (2/5  +  2/7))   sin  45   - 

((2/2  +  2/io)  -  2/6  j  sin  90°] 
^5    =  J^  [(2/1  +  2/n)  sin  75°  +  (2/2  +  2/10)  sin  30°  --  (2/3  +  2/9) 

sin  45°    -  (1/4  +  2/s)  sin  60°  +  (2/5  +  2/7)  sin  15°  +  y6  sin  90°] 

AT    =  %  [(2/1  +  2/n)  sin  75°  --  (2/2  +  2/io)  sin  30°  --  (2/3  +  2/9) 

sin  45°  +  (2/4  +  2/s)  sin  60°  +  (2/5  +  2/7)  sin  15°    -  y,  sin  90°]. 

Cosine  Terms. — The  cosine  terms  may  be  treated  in  a  similar 
manner. 

/0  N  kir  mkw 

As  -  cos  (2n  -  m)  ^  =  cos  2^  (19) 

the  differences  of  the  ordinates  are  involved. 
The  equation  corresponding  to  (18)  is 

+  cos  (2n  -  k)  —^  =  cos  k  ~  (20) 

The  sign  of  the  left-hand  member  is  +  if  m  is  even  and  —  if 
m  is  odd.  Applying  the  above  and,  for  convenience,  expressing 
the  results  in  terms  of  the  sines  of  the  angles,  the  values  of  B 
are 

Bi    =  1A  [2/o  sin  90°  +  (2/1  -  yn)  sin  75°  +  (2/2  -  2/10)  sin  60°  + 

(2/3  -  2/9)  sin  45°  +  (2/4  -  2/s)  sin  30°  +  (2/5  -  2/7)  sin  15°] 
#11  =  H  feo  sin  90°    -  (2/1  -  2/11)  sin  75°  +  (2/2  -  2/10)  sin  60°  - 

(2/3  -  2/9)  sin  45°  +  (2/4  -  2/s)  sin  30°  -  (yb  -  y7)  sin  15°] 
#3    =  H[{(yi   --   2/n)    ••    (2/3   --   2/9)    ••    (2/5   --   2/7)!  sin  45°  + 

!2/o  -  (2/4  -  2/s)}  sin  90°] 
#9    =  V*  [{-  (2/1  ~  2/n)  +  (2/3   -.2/9)  +  (2/5  -  2/7)!  sin  45°  + 

(2/0  -  (2/4  -  2/s)  1  sin  90°] 
#5  =  V*  [2/o  sin  90°  +  (2/1  -  2/11)  sin  15°    -  (y2  -  y10)  sin  60°  - 

(2/3  -  2/9)  sin  45°  +  (2/4  -  2/s)  sin  30°  +  (y.  -  2/7)  sin  75°] 
87    =  y*  [2/o  sin  90°    -  (2/1  -  2/n)  sin  15°  --  (2/2  -  2/10)  sin  60  + 

(2/3  -  2/9)  sin  45°  +  (2/4  -  2/s)  sin  30°  -  (2/5  -  2/7)  sin  75°]. 


DETERMINATION  OF  WAVE  FORM  655 

The  calculations  may  be  systematized  by  the  use  of  properly 
prepared  forms  such,  for  example,  as  that  following. 

The  numerical  work  may  be  checked  by  using  particular  values 
of  0. 


2/o  =  (Bi  +  #11)  +  (#3  +  #9)  +  (B6  +  B7) 
2/6  =  (A,  -  An)  -  (A,  -  A9)  +  (A6  -  A7) 
2/3  +  2/9  =  2  sin  45°  [(Al  +  An)  +  (A3  +  A9)  -  (A8  +  A7)] 
7/3-2/9  =  2  sin  45°  [(B,  -  Bn)  -  (B>  -  B9)  -  (Bb  -  B7)] 
2/4  +  2/8  =  2  sin  60°  [(A,  -  Au)  -  (A,  -  A7)} 

Following  the  plan  outlined  above,  schedules  corresponding  to 
any  number  of  measured  ordinates  may  be  prepared.  If  even 
harmonics  be  present  it  is  necessary  to  divide  the  whole  wave 
into  2n  parts. 

The  values  of  the  coefficients  A  and  B,  obtained  as  above  by  the 
use  of  a  definite  number  of  measured  ordinates,  determine  a 
curve  which  coincides  with  the  original  curve  at  the  measured 
points  and  diverges  from  the  original  curve  at  intermediate  points; 
consequently  the  more  complicated  the  wave  form,  the  greater 
the  number  of  ordinates  which  must  be  used.  A  schedule  based 
on  18  instead  of  12  ordinates  is  frequently  necessary.  As  a  check 
on  the  sufficiency  of  the  analysis,  values  of  y  intermediate 
between  the  measured  values  should  be  calculated  and  compared 
with  the  actual  ordinates  at  the  same  points. 


656 


ELECTRICAL  MEASUREMENTS 


ILLUSTRATION  OF  THE  USE  OF  A  TWELVE-POINT  SCHEDULE  FOR 

THE   ANALYSIS    OF   WAVES   CONTAINING    ONLY 

ODD    HARMONICS 

*ff  -  271  =  F2  ^  15°' 


FIG.  413. — E.M.F.  wave  of  small  alternator. 


The  e.m.f .  wave  of  a  small  alternator  is  shown  in  Fig.  413.  To  analyze 
this  wave  twelve  equally  spaced  ordinates  were  measured;  their  values  are 
entered  in  the  form  below, 


2/o  =  0.80 

2/i  =    8.50 
2/ii  =    8.70 

2/2    =    14-50 

2/io  =  15.40 

2/3  =  00.^0 
2/9  =  05.00 

Sums 

2/i  +  2/11  =  17.20 

2/2  +  2/io  =  32.70 

2/3  +  2/9  =  45.50 

Differences 

2/i  -  2/11  =  -  0.20 

2/2  —  2/10  =  —  4-10 

2/3  -  2/9  =  —5.40 

2/4  =  05.15 

2/5  =  29.  80 

2/6  =  30.05 

2/8  =  50.70 

2/7  =  32.90 

2/o  =    0.30 

Sums  2/4  +  2/8  =  55.55        2/s  +  2/7  =  50.70         2/0+  2/e  = 

Differences        2/4  —  2/s  =  —  4-55     2/s  —  2/7  =  —3.10 


.55 


Calculation  of  AI  and  An 

(yi  _|_  2/11)  gin  15°  -  (^7  #)    o  2588  =                  —  > 

(ys  _|_  yg  )  sin  45°  =  (46.6)    0.7071  =  -> 

32  951 

(2/5  +  2/7  )  sin  75°  =  (50.7)    0.9659  =  -» 

60.562 

(2/2  +  2/10)  sin  30°  =  (30.7)    0.5000  =  

) 

16.850 

(y4  _j_  ^8  )  gin  60°  =  (55  85)  0  8660  = 

> 

49  238 

2/6     sin  90°  =  (30  05)  1  0000  = 

_^ 

32  250 

Sums       

(97  965)  i 

(97  833)  2 

(97  .96  5)  i 

(97.  965)  i 

(97. 


Sum 


1S5.755  =  6A] 


Difference 


0.000 


DETERMINATION  OF  WAVE  FORM  657 

Calculation   of   As  and   Ag 
•yi  +2/11   =17.20 

2/3  +  2/9    =46.60 


Sum  =63.80 

2/5  +  2/7  =  00.70 

Difference      =    1.10 

+2/u)  +  (2/3  +  2/9)  -  (2/5  +  2/7))  sin  45°  =  (1.1)0.7071  =  (0.775), 
2/2  +2/io   =  30.70 
2/6  =  32.25 


Difference     =    0.45 

{ (2/2  +  2/io)  -  2/e }  sin  90°  = (0. 450}, 

(0.778)  i  (0.778], 

(0.450)2  (0.450)2 


Sum  1.228  =  643  Difference          0.328  = 

A3  =  0.005  A9  =  0.055 


Calculation  of  A&  and  A^ 

(2/i  +  2/n)  sin  75°  =  (17.2)  0.9659  =        10.013 
(2/s  +  2/v  )  sin  15°  =  (62.7)  0.2588  =         10.007 


Sum  =        32.840 
(2/3  +  2/9  )  sin  45°  =  (4$ .6)  0.7071  =        30. £51 


Difference  =  (  -  0.111], 

(2/2  -  2/io)  sin  30°  =  (30.7)  0.5000  =         16.35 
7/6   sin    90°  = =        30.05 


Sum  =         48.600 
(2/4  +  2/8  )  sin  60°  =  (50.85)0.8660=        ^.030 


Difference  =  (  -  0.030) 2 
(  -0.111],  (  -0.111], 

(  -  0.632)^  (  -  0.1 


Sum  -0.743  =  QA6  Difference          +0.501 

A&  =  -  0.104  Ai  =  +0.087 


42 


658 


ELECTRICAL  MEASUREMENTS 


Calculation  of  B\  and  B\\ 


Vo 

=  (  +  0  30) 

i  ooo  =     .    —  >• 

0  300 

?/io)  sin  60° 

=  (  -  4-10) 

0.8660  =  -+ 

-  3.551 

(2/4- 

2/8  )  sin  30° 

=  (  -4-55) 

0.5000  =  -> 

-  2.275 

(2/1  - 

2/n)  sin  75° 

=  (  -0.20) 

0.9659  =  -> 

-  0.193 

(2/3- 
(w5  - 

2/9  )  sin  45° 
2/7  )  sin  15° 

=  (-5.4  ) 

=  (—31   ) 

0.7071  =  
0  2588  = 

-  0  802 

Sums 

(  -5  526)i 

(  —  4  813)* 

(  - 

5.526)l 
4-813)* 

(  -  5.526)i 
(  -  4-813)* 

Sum 


-  10.339 

=  -    1 . 723 


Difference          -0.713 
Bn  =   -  0.119 


6£ 


Calculation  of  B3  and  B9 

2/3    -   1/9    =     -5.40 

ys  -  2/7  =  -  5.^0 


Sum 


=  -  8.50 


Difference     =  -8.30 

-  (2/i  -  2/n)  +  (2/3  -  2/9)  +  (2/5  -  2/7))  sin  45°  =  (  -  8.30)  0.7071  = 

(  -  5.869)* 
2/4-2/8  =   -4-55 
2/o  =        0.30 


Sum 


Difference  =   —4-85 
(2/4  -  2/s)  -  2/o)  sin  90°  = 


Difference 


(  -    5.869)* 

-  10.719  =  - 
#3  =   -1.786 


-  5.869)* 

+  1.019  =  -  6B9 
-  0.170 


Sum 


DETERMINATION  OF  WAVE  FORM 

Calculation  of  B5  and  B7 

2/o =  0 . 300 

(1/4  -  2/8  )  sin  30°  =  (  -  4.55)  0.5000  =       -  2.275 


659 


(2/2  - 


sin  60 


Sum  =      -1.975 

(  -  4.1   )  0.8660  =      -  3.551 


Difference     =    (  +  1.576)i 

(2/i  -  yn)  sin  15°  =  (  -  0.20)  0.2588  =      -  0.052 
(i/5  -  2/7  )  sin  75°  =  (  -  3.1   )  0.9659  =      -  2.994 


Sum  —  3.046 

0/3  -  2/9  )  sin  45°  =  (  -  5.4  )  0.7071  =      -  3.818 


(1.576), 
(0.772)2 

2.348  =  QB5 
Bb  =  0.391 


Difference          (  +  0 . 77. 
(1.576), 
(0.772)2 


Difference  0.804  = 

£7  =  0.134 


Checks,  see  page  655 


1J  \  •                       J. 

B3  1.786 

Bb  0.391 

B1  0.134 

B3  0.1701 


Ai    =      32.633 
An    =        0.022 


(32.611)1 
(-0.211), 


|Sum  = (32.655)i        Diff.     [5* .  £*£]  1 . 732 

j  Difference  =    (82.611)t  =56.84 

A3    =       0.204 

Ag    =       0.055  From  curve  yt-\-ys  =  66.85 


Sums  2.311      2 
Net  sum  0 . 299 
o  =  0.300 


'  1  Difference  =      (0.149)\ 


(0.259)3 


Sum 32.914 

Az=  -  0.124 
AT=  +  0.057 


ISum (-  0.037)6 

Difference  =    (-O.ISll)t 

Difference (32.961) 

(32.951)  (1.414)   -  46.69 
From  curre  yi  +  ]/*   -  46.60 


Sum       82.400 

(0.140)4 


Diff.      [32.251] 
From  curve  yt<"SS. 


660 


ELECTRICAL  MEASUREMENTS 


B3  =        1.78 
B9  =  -  0.17 

Difference (  +  1 . 95}i 

B,  =  0.39 
B7  =  0.13 


Difference.. 
Sum... 


(0., 


2.21 


#!  =   -  1.720 
Bu  =  -  0.119 

Difference...  .  .(  -  1.601], 


Difference 
From  curve, 


.[  +  3.81]IA14:  =  +  £.37 
•     ~  (2/3  -2/9)     =  +5.40 


=  V(32.633)2  +  (1.72)2  = 
32.678 


C3  =V  (0.204)2+  (1.78)2  = 

1.798 

C5  =  \/(0.124)2  +  (0.391?  = 

0.410 

C7=V(0.087)2+(0.134p  = 

0.160 

C9  =  \/(0.055)2+(0.170)2  = 

0.179 

Cn  =  V(0.022)2-h(0.119)2  = 

0.121 


tan  *  ~A~  —  tan  * 


tan"1  /r  =  tan~: 


-1.72 


+  32.633 

-  3.°02 
+  1.78 
+0.204 

+  83.°5 
+0.391 


tan  1  A    —  tan      _Q  224  ~~ 
+  107. 


tan" 


=  tan" 


+0.134 


+0.087 

+  57.c 

J59  -0.170  _ 

tan  l  j~  =  tan  1   IQ  055  ~ 

-72/ 
Bn  _x  -0.119  = 

-79.( 


Therefore  the  equation  of  the  curve  is 

e  =  32.678  sin  (co£  -  3.°02)  +  1.798  sin 
+  0.410  sin  5(co£  +  21.°52)  +  0.160  sin 
+  0.179  sin  9(co*  -  8.°0)  +  0.121  sin 


+  27.°8) 

+  8.°14) 
-  7.°2) 


DETERMINATION  OF  WAVE  FORM  661 

Fischer-Hinnen  Method  of  Analysis.10 — A  convenient  method 
of  harmonic  analysis  and  one  in  which  the  arithmetical  work 
is  reduced  to  a  minimum  is  due  to  Fischer-Hinnen ;  the  procedure 
is  based  on  two  mathematical  laws  which  are  demonstrated 
below. 

Suppose  a  wave  has  been  plotted  and  the  length  ab  (Fig.  414), 
is  that  of  a  complete  cycle,  or  360°  of  the  fundamental.  Then 
between  a  and  b  there  will  be: 

1  complete  period  of  the  fundamental 
3  complete  periods  of  the  third  harmonic 
5  complete  periods  of  the  fifth  harmonic. 

Denote  by  k  the  number  of  complete  periods  of  any  harmonic 
comprised  between  a  and  b.  Then 

k  =  1  for  the  fundamental 
k  =  3  for  the  third  harmonic 
k  =  5  for  the  fifth  harmonic. 


The  equation  of  the  sine  curve  corresponding  to  any  particular 
harmonic  will  be 

Y  =  Ak  sin  k  (0  +  a) 

where  both  6  and  a  are  expressed  in  degrees  of  the  fundamental. 
Now  let  a6,  which  corresponds  to  a  whole  wave,  be  divided  into 
P  equal  parts  and  P  ordinates  erected,  the  first  being  coincident 
with  a.  In  Fig.  414 

k  =  3,  and  P  =  7. 

i 
a 

— J«C  ^ 860°  of  Fundamental 


FIG.  414. — Pertaining  to   Fischer-Hinnen   method   of  harmonic  analysis. 

k  =  3,  P  =  7 

Denote  the  various  ordinates  thus  [YP]i,  [YP]z  .  .  .  ;  the  sub- 
script, P,  within  the  bracket  shows  the  number  of  sections  into 
which  the  base  ab  is  divided,  while  the  subscript  outside  the 


662  ELECTRICAL  MEASUREMENTS 

bracket  shows  the  number  of  the  particular    ordinate   under 
consideration. 

[Yp]i  =  Ak  sin  ka 

360° 


[YP]2  =  Ak  sin  \k  —p-  +  ka) 

(*}fif)°  \ 

2k-™-+  ka) 


(Qflf)0  v 

(P  -  1)  k     p  -  +   ka)  . 

Then  the  sum  of  the  P  ordinates  is 

[YP]i  +  [7p],  +  [7p],  +  .    .    .  +  [FP]p  = 

[   -     7      (1  /fc360°\  _  //c360°\ 

A*  \sm  ka  1  1  +  cos  (    p    )  +  cos  2  \—p—j  + 

,  //c360°\  1X  //c360°\  1 

cos  3  (—p—)  f  -    -    .  +  cos  (P    -  1)  (—  p  —  j  I  + 

f  .     //c360°\  _  /fc360°\ 

cos  ka    I  sin  (  —p  —  1  +  sin  2  (  —  -  p  —  )  + 

,  //c360°\  nN  /fc360°\  n 

sin  3  •  (~^—  j  +  -    -    -  +  sin  (P  -  1)  (-p—  )  )  J*  (21) 

/b 
Inspection  shows  that  if  p-  is  a  i^/ioZe  number, 

[Fpli  +  [FP]2  +  [7p]8  +  .    .    .  +  [YP]P  =  PAksm  ka  =  P^p], 

(22) 

k 
That  is,  when  ^  is  a  whole  number  the  sum  of  P  equally  spaced 

ordinates  is  equal  to  P  times  the  first  ordinate.     This  is  the  first 
of  the  laws  referred  to  above. 

k 
If  ^  is  not  a  whole  number  the  above  series  can  be  summed  by 

aid  of  the  following  trigonometrical  formulae. 

cos  B  +  cos  26  +  cos  30  +  .    .    .  +  cos  (P  -  1)0  = 


sin  6  +  sin  20  +  sin  30  +  .    .    .'  +  sin  (P  -  1)0  = 

.     (P  -  1)0    .    P0 
sin  --  -=  ----  sin  -= 


-r       <24> 

Sin2 


In  this  case  when 


DETERMINATION  OF  WAVE  FORM  663 

/c360°          k 
6  =  ~~p~~,  and  -p  is  not  a  whole  number,  both  the  series  in  (21) 

reduce  to  zero. 
Consequently 

[Fp],  +  [YP],  +  [Yp],  +  +  (YP]P  =  0  (25) 

That  is,  when  p  is  not  a  whole  number  the  sum  of  P  equally 

spaced  ordinates  is  zero.  This  is  the  second  of  the  two  laws  upon 
which  this  method  depends. 

These  relations  are  used  as  follows:  The  wave  is  plotted  and 
any  point  is  taken  as  the  origin. 

At  the  origin,  t  =  0,  all  the  sine  terms  are  zero  and  all  the  cosine 
terms  have  their  maximum  values,  that  is,  BI,  Bs,  Bb  .  .  .so 

r,  =  BI  +  BS  +  B,+  .  .  . 

To  find  Bs:— 

Between  a  and  b  there  are  three  complete  periods  of  the  third 
harmonic,  nine  complete  periods  of  the  ninth  harmonic,  fifteen 
complete  periods  of  the  fifteenth  harmonic,  and  so  on. 

Divide  the  base  ab  into  three  equal  parts.     Then  P  =  3  and 

k 

p  =  1  for  the  third  harmonic 

k 

p  =  3  for  the  ninth  harmonic 

^     =  5  for  the  fifteenth  harmonic. 


These  are  all  whole  numbers  and  by  (22) 

[F3]i  +  [F3]2  +  [F3]3  =  3[£3  +  B,  +  B16  +  J521  +  .  .  .] 
To  find  Bb:— 

Divide  the  base  ab  into  five  equal  parts,  P  =  5  ;  between  a  and 
b  there  are  five  complete  periods  of  the  fifth  harmonic,  fifteen 
of  the  fifteenth  harmonic,  so 

-p  =  1  for  the  fifth  harmonic 

-p  =  3  f  or  the  fifteenth  harmonic. 


Consequently 
Ji  +  [F5]2  + 


664  ELECTRICAL  MEASUREMENTS 

Similarly  by  dividing  the  base  into  seven  and  into  nine  equal 
parts, 

[77],  +  [F7]2  +  [F7]3  +•  - .+  [F7]7  =  7[B7  +  £21  +  B35.  .  .] 
[FJi  +  [F9]2  +  [F9]3  +.'..+  [F9]9  =  9[£9  +  £27  +  £45-  .  •] 

It  is  convenient  to  erect  the  first  ordinate  at  the  point  where 
the  curve  crosses  the  axis.  In  that  case  Yi  =  0  and 

Bt  +  £3  +  #5  +  Bi  + .  .  .  =  0 

In  practice  the  process  is  somewhat  simplified,  for  except  in 
special  cases  the  harmonics  above  the  seventh  are  not  important. 
So 

#3=^2  [F3]  approximately 
B5  =  \i  ^  [Yt] 

B,  =  M  S  [F7] 
B,  =  y9~S  [F.] 
BI  =  —  BZ  —  Bz  —  BT. 

When  these  approximations  are  used,  by  appropriately  divid- 
ing the  base,  tests  may  be  applied  to  detect  the  presence  of 
higher  harmonics.  If  they  are  present  the  approximate  values 
of  the  lower  harmonics  may  be  corrected;  for  instance,  if  the  9th 
be  present,  then 

£3  =  M  S  [7,]  -  Bg 

To  find  A i,  As,  etc. 

As  these  are  the  coefficients  of  the  sine  terms,  which  will  have 
their  maximum  values  a  quarter  period  from  the  initial  ordinate 
[YP]i,  draw  the  first  of  the  new  set  of  ordinates  [YP]\  a  quarter 
period  from  [YP]i.  At  this  point,  all  the  cosine  terms  are  zero 
and  consequently  add  nothing  to  the  value  of  the  ordinate. 

The  initial  ordinate  of  the  fundamental,  as  well  as  that  of  the 
fifth  and  of  the  ninth  harmonic,  is  positive,  while  the  initial 
ordinate  of  the  third  and  of  the  seventh  harmonic  is  negative. 

F'i  =  Al  -  Az  +  A5  -  A7  +  A9. . . 

When  the  base  has  been  divided  into  three,  five,  seven,  etc., 
equal  parts,  by  the  rules  already  given, 

[FJ'i  +  [F3]'2  +  [F8]'8  =  3  [-  A3  +  A,  -  An.  .  .] 
IFJ'i  +  [F5]'2  +  [F5]'3  . . .  +  [F5]'5  =  5  [A 5  -  Aw. , .] 
[F7]'i  +  [F7]'2  +  [F7]'3  . . .  +  [F7]'7  =  7  [-  A7 
[FJ'i  +  [F9]'2  +  [F9]'8  +  .  • .  +  [F9]'9  =  9  [A 9 


DETERMINATION  OF  WAVE  FORM  665 

Therefore, 

^3  =  ~  M  2  [Fs]'  approximately 

Ab=        X2[Yb}' 

A7  =  -  }/7  S  [Y7]f 

A,=       %  S  [F9]' 

1Y  =  A1  -  A3  +  A5  -  A7  +  A9  .... 

When  dealing  with  waves  containing  only  the  odd  harmonics, 
it  is  necessary  to  plot  only  one-half  the  wave,  since  the  second 
half  is  like  the  first  with  the  algebraic  sign  of  the  ordinates 
reversed.  Suppose  the  half  wave  has  been  divided  into  2k  parts, 
equivalent  to  dividing  the  whole  wave  into  4fc  parts,  then  the 
ordinate  [FJi  is  identical  with  [F4fc]i.  The  relation  of  the  num- 
ber, NM,  of  any  ordinate  when  the  whole  base  is  divided  into  4fc 
parts  to  the  number  of  the  same  ordinate,  Nk,  when  the  whole 
base  has  been  divided  into  k  parts  is  given  by 


-  1)  +  1  =  4tf*  -  3  =  N,k.  • 
Consequently 

BS  =  y3  [[Fiji  +  [F12]5  +  [F12]9]  =  y*  [[Fiji  +  [F12]5  -  [F12]3] 

#5  =  }i  [[F20]i  +  [F20]5  +  [F20]9  -  [F20]3  -  [F20]7] 

£7  =  M  [[F2Ji  +  [F28]5  +  [F28]9  +  [F28]13  -  [F28]3  -  [F28]7 

-  [F28]n]. 

When  the  sine  coefficients  are  determined,  the  ordinate  [FJ;i  is 
identical  with  [F4A;]&+iforwhen  the  sine  terms  are  determined  the 
initial  ordinate  is  transferred  k  spaces  to  the  right.  In  this  case 
the  number  of  any  ordinate,  A7"^,  when  the  whole  base  has  been 
divided  into  4k  parts  is  related  to  the  number  of  the  same 
ordinate,  JV'*,  when  the  whole  base  has  been  divided  into  k 
parts,  as  follows  : 


-  1)  +  k  +  1=  4#'*  -  3  +  k  =  N^ 
So 
As  =  -  H  [[^iJ4  +  [F1218  +  [F12]12]  =  -  y3  [[F12]4  -  [F12]2  - 

[F12]6] 

A5  =  1A  [[F20]2  -  [F20]4  +  [F20]6  -  [F20]8  +  [F20]io] 
A7  =  M  [  -  t^8]2  +  [F28]4  -  [F28]6  +  [F28]8  -  [F28]10  + 

[F28]i2  —  [F2s]i4J. 


666  ELECTRICAL  MEASUREMENTS 

To  combine  the  sine  and  cosine  terms, 

[ft  -i 
kut  -f  tan"1  -p 

=  Ck  sin  fc    orf  4- 


+  BI 

Bk 

tan  ^  =  ^ 

(pk  is  positive  if  the  ascending  portion  of  the  component  curve 
first  cuts  the  axis  at  the  left  of  the  origin. 

Harmonic  Analyzers.  —  There  are  other  methods  of  harmonic 
analysis,13  but  it  is  evident  that  the  labor  involved  in  such 
work  is  very  considerable  and  becomes  formidable  if  an  in- 
vestigation is  in  hand  which  requires  the  treatment  of  many 
curves.  Cases  arise  where  curves  other  than  those  of  e.m.f.  and 
current  must  be  analyzed  and  it  is  necessary  to  be  able  to  include 
both  the  odd  and  the  even  harmonics.  Hence  the  need  in 
practical  work  of  machines  by  which  the  analysis  may  be 
effected.  References  to  descriptions  of  a  *  number  of  these 
harmonic  analyzers  are  given  at  the  end  of  this  chapter. 

A  simple  form  of  harmonic  analyzer,  particularly  designed 
for  electrical  engineering  work  has  been  described  by  Chubb.11 
Its  action  may  be  explained  as  follows. 

On  page  650  attention  was  called  to  the  fact  that  the  exact 
expressions  for  Ak  and  Bk  are 

Ak  =  -  I  f($)  sin  k6  dd 

K  JO 

and 


Bk  =  -  I  /(0)  cos  ke  dd. 

TTJQ 

Referring  to  Fig.  415,  if  the  point  P  be  given  a  displacement 
along  the  horizontal  axis  always  equal  to  /(0),  and  if  at  the  same 
time  it  experiences  a  perpendicular  displacement  always  propor- 
tional to  sin  (kO),  then 
x  =  fe 

y  =  R  sin   kO,  where  R  is  the  maximum  displace- 
ment along  y, 

dv  =  kR  cos  ke  dd 


DETERMINATION  OF  WAVE  FORM 


667 


FIG.  415. — Chubb  harmonic  analyzer,  Westinghouse  Co.  B,  analyzer 
set  for  determining  cosine  components;  C,  analyzer  set  for  determining  sine 
components. 


668  ELECTRICAL  MEASUREMENTS 

and  the  area  of  the  curve  traced  while  6  goes  through  a  complete 
cycle  will  be 

area  =  kR  I  fd  cos   k8  do. 

Jo 
Consequently  by  (11) 

area 
Bk  =   dfcTT 

Similarly  if  the  vertical  displacement  of  P  is  given  by 
y  =  R  sin  (kB  -  |)   =  -RcoskB 
dy  =  kR  sin  0  d0, 

and  the  area  of  the  curve  traced  by  P  will  be 

/•a, 

area  =  Rk     /(0)  sin  d  dd. 
Jo 

Consequently 

.         area 


The  Chubb  analyzer  is  a  mechanism  for  mechanically  calculat- 
ing Ak  and  5fc  in  the  manner  just  described.  The  areas  of  the 
curves  are  determined  by  a  planirrieter  as  is  indicated  in  Fig.  415. 
The  arrangement  by  which  the  point  P  is  guided  is  shown  in  a 
general  way  in  Fig.  415,  B  and  C.  The  first  step  in  using  the 
analyzer  is  to  cut  out  a  bristol  board  template  which  represents 
/(0),  such  as  is  shown  in  Fig.  415,  D.  The  circle  abc  is  the  base  line 
from  which  the  values  of  /(0)  are  measured,  +  values  of  /(0) 
being  measured  radially  outward  and  —  values  radially  inward. 

The  template  is  mounted  on  the  turntable  T,  and  the  pin  E 
on  the  movable  transverse  rod  BP  is  forced  against  the  edge  of 
'the  template  by  springs.  Obviously  if  the  turntable  rotates, 
the  point  P  experiences  a  displacement  x  =/(0). 

The  frame  which  carries  the  turntable  and  the  mounting  for 
the  rod,  BP,  slides  on  the  ways,  RR}  and  by  means  of  a  crank 
and  slotted  crosshead  can  be  given  a  sinusoidal  displacement 
along  these  ways. 

Rotary  motion  is  communicated  to  the  turntable  by  means  of 
a  wormwheel  mounted  on  the  axis  of  the  turntable,  and  a  worm 
which  slides  on  a  splined  shaft  placed  parallel  to  the  ways. 

By  means  of  a  system  of  change  gears  the  frame  carrying  the 


DETERMINATION  OF  WAVE  FORM  669 

turntable  may  be  caused  to  make  k  complete  displacements 
along  the  ways  while  the  table  makes  one  complete  revolution. 
The  point  P  is  thus  guided  in  the  manner  already  suggested. 

When  the  sine  components  are  to  be  determined  the  crank  is 
placed  so  that  the  carriage  is  at  its  maximum  displacement, 
at  the  lower  end  of  the  ways,  when  6  =  0.  If  the  cosine  terms 
are  desired  the  carriage  is  started  at  its  mid-position  when  6  =  0. 

By  the  use  of  the  proper  system  of  change  gears  the  coefficient 
of  any  harmonic,  either  odd  or  even,  is  readily  determined  with 
all  the  accuracy  needed  in  electrical  engineering  work. 

The  oscillograph  is  readily  adapted  for  obtaining  curves  plotted 
in  the  peculiar  manner  necessary  for  the  construction  of  the  tem- 
plate; the  oscillogram  is  taken  on  a  plate  which  is  rotated  about 
an  axis  perpendicular  to  its  plane.  If  undeflected  the  spot  of 
light  traces  the  base  circle  abc  from  which  the  displacements  are 
measured. 

From  the  oscillogram  one  can  readily  detect  the  presence  of 
even  harmonics,  for  if  they  are  absent  all  the  "diameters"  are 
of  equal  length  and  equal  to  the  diameter  of  the  base  circle  abc. 

Experimental  Analysis:  Laws  Method.12 — When  dealing  with 
potential  difference  and  current  waves  it  is  possible  to  determine 
the  various  coefficients  experimentally  as  will  be  seen  from  the 
following. 

The  coefficient  Ak  is  twice  the  mean  product  between  +  TT  and 
— TT  of  the  curve  /(0)  and  the  curve  sin  k9;  Bk  is  twice  the  mean 
product  of  /(0)  and  cos  kO,  between  the  same  limits.  The  deflec- 
tion of  an  electrodynamometer  is  proportional  to  the  mean  prod- 
uct of  the  currents  in  the  fixed  and  movable  coils.  Conse- 
quently, if  the  wave  to  be  analyzed,  of  frequency  /,  is  led 
through  the  fixed  coil  while  a  sinusoidal  current  wave  of  fre- 
quency kf  and  maximum  value  A'k  is  sent  through  the  movable 
coil,  the  deflection  of  the  instrument  will  be  proportional  toAk  or 
to  Bk  according  as  the  zero  point  of  the  unknown  wave  coincides 
with  the  zero  point  of  the  sine  wave  or  with  the  maximum  of 
the  sine  wave.  The  deflection  will  be  proportional  to  Ck  if  the 
phase  of  the  sinusoidal  current  is  adjusted  until  the  deflection  is 
a  maximum. 

,In  order  to  carry  out  the  analysis,  the  machine  from  which  the 
sinusoidal  current  is  derived  must  be  driven  from  the  shaft  of 


670  ELECTRICAL  MEASUREMENTS 

the  generator  by  means  of  change  gears  which  permit  the  speed 
to  be  varied  so  that  the  frequency  may  be  made  1,  3,  5,  7  .  .  . 
times  that  of  the  main  current.  Also  the  machine  must  be  so 
constructed  that  the  phase  of  the  sinusoidal  current  may  be  al- 
tered at  will,  a  scale  being  provided  so  that  the  phase  displacements 
are  readily  determined. 

The  maximum  value  of  the  sinusoidal  current,  A'k,  is  de- 
termined from  the  reading  of  a  current  dynamometer.  The 
process  of  making  a  measurement  is  to  change  the  phase  of  the 
machine  giving  the  sinusoidal  current  until  the  dynamometer 
stands  at  zero,  then  to  shift  the  phase  90°  and  take  the  dynamo- 
meter reading.  A  contact  arrangement  and  galvanometer  which 
by  means  of  a  double-throw  switch  may  be  connected  to  the 
terminals  of  non-inductive  resistances  in  either  the  main  circuit  or 
in  that  of  the  sine  generator,  permits  the  zero  points  on  the  waves 
to  be  located.  The  phases  of  the  harmonics  may  then  be  de- 
termined from  the  readings  on  a  scale  of  degrees  attached  to  the 
movable  field  frame  of  the  sine  dynamo. 

The  disadvantage  of  this  method  is  that  it  requires  special 
apparatus. 

References 

1.  "Sur  les  Courants  Alternatifs  et  la  Force  Electromotrice  de  1'Arc 
Electrique,"  J.  JOUBERT,  Journal  de  Physique,  vol.  9,  1880,  p.  297. 

2.  "An   Apparatus   for   Recording   Alternating-current    Wave    Forms," 
F.  A.  LAWS,  Proc.  American  Academy  of  Arts  and  Sciences,  vol.  36,  1901, 
p.  321.     "The  Slow  Registration  of  Rapid  Phenomena  by  Stroboscopic 
Methods,"  E.  HOSPITALIER,  Journal  Institution  of  Electrical  Engineers,  vol. 
33,  1903,  p.  80.     See  also  Electrician,  vol.  52,  1903-04,  p.  298.     "Mechan- 
ical Integration  of  the  Electromotive  Force  When  Even  Harmonics  are 
Present,"  M.  MORRISON,   Southern  Electrician,  vol.  43,  1911,  p.  60.     "The 
Oscillograph  and   Its  Uses,"  L.   T.  ROBINSON,  Trans.  American  Institute 
Electrical  Engineers,  vol.  24,  1905,  p.  185. 

3.  "A  New  Method  of  Tracing  Alternating-current  Curves,"  F.  TOWN- 
SE.ND,    Trans.   American  Institute  Electrical  Engineers,  vol.  17,  1900,  p.  5. 
"The    Use    of    the    Synchronous    Commutator    in    Alternating-current 
Measurements,"  FREDERICK  BEDELL,  Journal  of  the  Franklin  Institute,  vol. 
176,  1913,  p.  385. 

4.  "An  Apparatus  for  Determining  the  Form  of  a  Wave  of   Magnetic 
Flux,"  M.  G.  LLOYD  and  J.  V.  S.  FISHER,  Bulletin  Bureau  of  Standards,  vol.  4, 
1908,  p.  467. 

5.  "Oscillographes,    nouveaux    appareils    pour    1'etude    des    oscillations 
electrique  lentes,"  A.  BLONDEL,  Comptes  Rendus,  vol.   116,  1893,  p.  502. 


DETERMINATION  OF  WAVE  FORM  671 

"Conditions  generates  qui  doivent  remplis  les  instruments  enregistreurs 
ou  indicateurs,"  A.  BLONDEL,  Comptes  Rendus,  vol.  116,  1893,  p.  748. 
"Oscillographs,"  W.  D.  B.  DUDDELL,  Electrician,  vol.  39, 1897,  p.  636.  "Ex- 
periments on  Alternate-current  Arcs  by  Aid  of  Oscillographs,"  W. 
DUDDELL  and  E.  W.  MARCHANT,  Journal  Institution  of  Electrical  Engi- 
neers, vol.  28,  1899,  p.  1.  "Some  Uses  of  the  Oscillograph,"  "Flux  Wave 
in  Transformers  and  Currents  in  Rotary  Converter."  D.  K.  MORRIS  and 
J.  K.  CATTERSON-SMITH,  Electrician,  vol.  52,  1904,  p.  684.  "Sur  les 
Oscillographes  et  methodes  d'enregistrement  des  courbes  de  courants 
alternatifs,"  H.  ABRAHAM,  L'Eclairage  Electrique,  vol.  12,  1897,  p.  180. 
"Rheographe,"  H.  ABRAHAM,  L'Eclairage  Electrique,  vol.  12,  1897,  p.  350. 
"The  Oscillograph  and  Its  Uses,"  L.  T.  ROBINSON,  Trans.  American  Insti- 
tute Electrical  Engineers,  vol.  24,  1905,  p.  185. 

6.  "An  Electrostatic  Oscillograph,"  H.  Ho  and  S.  KOTO,  Proc.  Physical 
Society,  London,  vol.  26,  1913,  p.  16. 

7.  "Ueber  ein  Verfahren  zur  Demonstration  und  zum  Studium  der  Zeit- 
lichen  Verlaufer  variabler  Strome,"  F.  BRAUN,  Annalen  der  Physik,  vol.  60, 
1897,  p.  552.     "Eine  Methode  zur  Demonstration  und  Photographic  von 
Stromcurven,"  J.  ZENNECK,  Annalen  der  Physik,  vol.  69,  1899,  p.  838.     "An 
Investigation  of  Dielectric  Losses  with  the  Cathode  Ray  Tube,"  JOHN  P. 
MINTON,  Proc.  American  Institute  of  Electrical  Engineers,  vol.  34,  1915,  p. 
1115. 

8.  "An  Elementary  Treatise  on  Fourier  Series  and  Spherical,  Cylindrical 
and   Ellipsoidal   Harmonics,"    WILLIAM   ELWOOD   BYERLY,    Ginn   &   Co., 
Boston,  1893. 

9.  "Methode  der  Zeriegung  in  Sinuswellen,"  C.  RUNGE,  Elektrotechnische 
Zeitschrift,  vol.  26,  1905,  p.  247.     "Harmonic  Analysis  Reduced  to  Sim- 
plicity," SYLVANUS  P.  THOMPSON,  Electrician,  vol.  55,  1905,  p.  78.     "The 
Analysis  of  Alternating-current  Waves  by  the   Method   of   Fourier  with 
Special  Reference  to  Methods  of  Facilitating  the  Computation,"  FREDERICK 
W.  GROVER,  Bulletin  Bureau  of  Standards,  vol.  9,  1913,  p.  567.     "A  Me- 
chanical Process  for  Constructing  Harmonic  Analysis  Schedules  for  Waves 
having  Even  and  Odd  Harmonics,"  HAWLEY  O.  TAYLOR,  Physical  Review, 
new  series,  vol.  vi,  1915,  p.  303. 

10.  "Methode    zur   schnellen    Bestimmung    harmonischer    Wellen,"    J. 
FiscHER-HiNNEN,  Elektrotechnische  Zeitschrift,  vol.  22,  1901,  p.  396. 

11.  "A  New  Harmonic  Analyzer,"  A.  A.  MiCHELSONand  S.  W.  STRATTON, 
American  Journal  of  Science,  vol.  5,  1898,  p.  1.     "The  Analysis  of  Periodic 
Waves,"  L.  W.  CHUBB,  The  Electric  Journal,  vol.  10,  1914,  p.  91.     "Polar 
and  Circular  Oscillograms  and  Their  Practical  Application,"  L.  W.  CHUBB, 
The  Electric  Journal,  vol.  1 1,  1914,  p.  262. 

12.  "Preliminary  Note  on  a  Method  for  the  Harmonic  Analysis  of  Alter- 
nating Currents,"  F.  A.  LAWS,  Technology  Quarterly,  vol.  6,  1893,  p.  252. 
"Resonance  Analysis  of  Alternating  Currents,"   M.  L.  PUPIN,  American 
Journal  of  Science,  vol.  48,  1894,  pp.  379,  473. 

13.  "Aufnahme   und   Analyse  von    Wechselstromkurven,"    E.    ORLICH 
Braunschweig,  1906,  Friedrich  Vieweg  &  Sohn. 


CHAPTER  XV 
CABLE  TESTING 

FAULT  LOCATION 

Continuity  of  service  is  essential  to  the  success  of  any  elec- 
trical undertaking,  whether  it  be  for  supplying  light  or  power. 
So  far  as  the  transmission  lines  are  concerned,  continuity  implies 
that  the  risk  of  interruption  has  been  reduced  to  a  minimum  by 
the  use  of  proper  methods  of  construction,  and  of  suitable 
materials,  such  as  cables,  insulators,  etc.  Even  when  the 
greatest  care  has  been  exercised  in  these  matters,  cables  will 
break  down,  line  wires  will  become  crossed  or  grounded  and 
insulators  will  be  punctured  or  broken. 

Accidents  which  interrupt  the  service  are  often  due  to  abnormal 
conditions,  over  which  one  has  no  control,  and  it  is  necessary 
to  have  means  of  locating  the  position  of  the  defective  parts  of 
the  lines  or  cables,  in  order  that  repairs  may  be  expeditiously 
made.  Newly  installed  power  cables  not  infrequently  break 
down  during  the  high-voltage  acceptance  tests,  and  these  breaks 
must  be  located. 

The  special  problem  of  locating  faults  in  long  submarine  cables 
is  discussed  in  such  works  as  Kempe's  "  Handbook  of  Electrical 
Testing,"  and  will  not  be  considered  here. 

In  general,  the  methods  here  treated  will  be  those  employed 
in  dealing  with  power  cables  in  cities,  and  with  telephone  and 
telegraph  lines,  and  it  will  be  assumed  that  only  one  fault,  or 
connection  to  ground,  exists. 

The  theory  underlying  the  methods  of  fault  location  is  very 
simple,  but,  on  account  of  constantly  varying  circuit  conditions, 
the  practical  execution  of  the  tests  requires  a  skill  and  judgment 
which  can  be  obtained  only  by  actual  experience. 

Location  of  Grounds  and  Crosses. — An  earth  fault,  or  ground, 
is  due  to  any  defect  in  the  insulation  of  the  conductor  which 
impairs  or  destroys  its  efficiency  so  that  a  current  may  pass 
from  the  wire  to  the  earth  or  to  the  cable  sheath.  A  cross  is  due 

672 


CABLE  TESTING  673 

to  the  impairment  of  the  insulation  between  two  wires  so  that 
the  current  may  pass  between  them. 

The  location  of  grounds  and  crosses  is  effected  by  the  same 
methods.  In  a  multiple-conductor  cable,  the  first  step  is  to  pick 
out  the  conductors  which  are  faulty,  for,  in  general,  some  con- 
ductors remain  in  perfect  condition. 

For  this  purpose,  both  ends  of  the  cable  are  disconnected  from 
the  service  apparatus,  and  the  insulation  resistances  between, 
the  various  conductors  and  ground  and  between  the  con- 
ductors themselves  are  measured;  the  voltmeter  method  may  be 
used.  If  the  faults  are  of  sufficiently  low  resistance,  bridge 
measurements  with  reversed  currents  may  be  made.  Continuity 
tests  should  also  be  made  to  determine  whether  any  of  the  con- 
ductors have  been  burned  off  or  broken.  The  above  tests  enable 
one  to  decide  on  the  subsequent  procedure. 

If  the  resistance  per  unit  length  of  the  line  is  uniform,  three 
things  must  be  known  in  order  that  a  ground  or  a  cross  may  be 
located: 

1.  The  total  length  of  the  faulty  line. 

2.  The  total  conductor  resistance  of  the  faulty  line  at  the  time 
of  test. 

3.  The  resistance  of  the  faulty  line  from  the  testing  station  to 
the  fault. 

The  length  of  the  line  is  given  by  the  office  records.  When 
there  are  only  two  wires  connecting  the  stations  at  the  ends  of 
the  line,  it  is  not  possibe  to  measure  the  line  resistance  after  the 
fault  has  occurred.  The  best  approximation  possible  must 
then  be  made  by  taking  the  stated  resistance  per  unit  length 
and  correcting  it  for  temperature;  in  this  correction  there  may 
be  considerable  uncertainty,  for  the  temperature  coefficient  of 
the  copper  is  large  (0.4  per  cent,  per  degree  C.)  and  it  is  often 
difficult  to  form  a  just  estimate  of  the  temperature  of  the  con- 
ductor, especially  if  it  is  in  a  duct  near  heavily  loaded  cables. 

Blavier  Test. — In  case  the  faulty  wire  is  the  only  one  connect- 
ing the  stations,  Blavier's  method  furnishes  the  only  means  of 
locating  the  fault  by  measurements  made  from  one  end  of  the 
line.  In  order  that  the  test  may  be  carried  out,  it  is  necessary 
that  the  observer  be  able  to  send  his  instructions  over  the  line 
to  the  attendant  at  the  other  end. 

43 


674  ELECTRICAL  MEASUREMENTS 

The  total  line  resistance  is  supposed  to  be  known  from  previous 
measurements  made  while  the  line  was  perfect;  denote  it  by  L. 

Two  measurements  of  the  resistance  to  ground  are  made  by  the 
observer  at  the  sending  end,  one,  R i,  with  the  far  end  insulated 
and  a  second,  Rz,  with  the  far  end  grounded.  Then,  referring 
to  Fig.  416, 

L  =  x  -f  y 
i        Ri  =  x  +  g 


-L  Ohms- 


Sending  !  I   Far 

End     k — x  Ohm8-          >|<  — V  Ohm* —        »-j  End 

>    g=  Kesistance 
|  to 

<  Ground 

Gxoujid 

FIG.  416. — Blavier  and  earth  overlap  tests  for  fault  location. 
Eliminating  g  and  y, 

x  =  R2~  VlLT-^HRi  -  R*)  (1) 

This  gives  the  resistance  from  the  sending  station  to  the  fault. 
The  corresponding  distance  is  calculated  by  aid  of  the  known 
resistance  per  unit  length  of  the  cable. 

The  resistance  measurements  may  be  made  in  any  convenient 
manner,  as  by  the  volt  and  ammeter  method.  A  practical 
difficulty  is  that  the  resistance  to  ground,  g,  is  variable,  being 
influenced  by  the  amount  of  moisture  present  and  the  action 
of  the  current  at  the  fault.  Also,  the  resistance,  g,  may  be  so  high 
that  it  exerts  very  little  shunting  action  when  y  is  placed  in 
parallel  with  it  by  grounding  the  far  end  of  the  line. 

The  Earth  Overlap  Test. — In  applying  this  test  it  is  neces- 
sary to  make  resistance  measurements  from  both  ends  of  the 
line.  With  the  far  end  grounded,  the  resistance,  12 1,  to  ground 
is  measured  from  the  near  end.  The  line  is  then  grounded  at 
the  near  end  and  the  resistance  to  ground,  #2,  is  measured  from 
the  far  end.  Then 
L  =  x  +  y. 

*—•-.-??• 


CABLE  TESTING 


675 


or 


X    = 


'y  = 


L-  R2 
RI  —  Rz 

LT> 
—    L\>\ 

T>  T) 

-Kz   —  K\ 


\  _     [R^L^-jKJ 

fei  (L  -"#7; 
\/  T>  (j    E> x 

\  /L  2  I  -L/    —   1L  i 


(2) 


(3) 


Practical  details  concerning  the  application  of  this  test  to  long 
submarine  cables  are  given  in  the  Journal  of  the  Institution  of 
Electrical  Engineers,  1885,  vol.  16,  page  581. 

The  Volt-ammeter  Test. — In  this  method  it  is  necessary 
to  have  between  the  testing  stations,  a  second  and  unfaulted 
conductor  which  can  be  used  as  a  potential  lead  to  the  far  end 
of  x. 


t 


WE 


FIG.  417. — Volt-ammeter  method  for  fault  location. 

In  Fig.  417  the  faulted  wire  is  shown  by  ab,  the  unfaulted  one 
by  dc;  V  is  a  voltmeter  and  A  is  an  ammeter.  With  these  con- 
nections a  regular  fall  of  potential  measurement  of  x  may  be 
made. 

The.  P.D.,  Vx,  between  the  terminals  of  x,  will  be  given  by 

V,  -7i 


where  Vi  is  the  reading  of  the  voltmeter  and  Rv  is  the  voltmeter 
resistance.  If  /i  is  the  reading  of  the  ammeter,  the  current 
through  x  will  be 

r      T     Vl 

I'-Il~  R- 

If  r  is  an  appreciable  fraction  of  Rv,  it  may  be  eliminated;  to 
do  this  transfer  the  ammeter  connection  to  d  and  make  a  second 
measurement.  Call  the  reading  of  the  voltmeter,  V2,  and  that  of 
the  ammeter.  72.  Then  the  voltage  accross  the  ends  of  r  is 


7-2. 

KV 


676  ELECTRICAL  MEASUREMENTS 

The  value  of  x  is 

X      =       -  y  —j y~ 

•*-  1  T>       '  ~     T       E> 


(4) 


If  an  electrostatic  voltmeter  is  used,  no  allowance  is  necessary 
for  the  voltmeter  current  and 

V 


Loop  Tests.  —  By  a  loop  test  is  meant  any  method  of  locating 
grounds  or  crosses  by  determining  the  resistances  of  the  two  sec- 
tions of  the  loop  formed  by  connecting  the  faulted  conductor  at 
its  far  end  to  an  unfaulted  conductor  which  returns  to  the  send- 
ing station  (see  Fig.  418). 


1 


FIG.  418. — Loop-test  for  locating  faults. 

The  grounded  conductor  is  represented  by  ab,  the  fault  being 
at  b'.  The  unfaulted  conductor  is  shown  by  dc]  at  the  far  end  it 
is  electrically  connected  with  the  faulted  conductor  by  a  low- 
resistance  jumper  which  must  be  insulated  from  ground.  It  is 
essential  that  the  contacts  at  b  and  c  be  perfect. 

The  superiority  of  the  loop  tests  is  due  to  the  fact  that  the 
results  are  independent  of  the  resistance  of  the  fault  itself. 


FIG.  419. — Two-ammeter  loop  test  for  locating  faults. 

Two-ammeter  Loop  Test. — In  this  method  the  two  sections 
of  the  loop  are  fed  in  parallel  from  the  same  battery  and  the 

SY* 

ratio  -  is  determined  from  the  readings  of  two  ammeters,  one 


CABLE  TESTING  677 

placed  in  series  with  x,  the  other  in  series  with  r,  as  indicated 
in  Fig.  419. 

.  The  resistances  of  the  two  ammeters  and  the  connections  are 
assumed  to  be  negligible.  The  polarity  of  the  battery  should  be 
such  that  the  fault  resistance  is  a  minimum.  If  the  readings 
of  the  ammeters  are  Ix  and  Ir, 

Lr    _    X  _  Ir  _  X 

Tx  ~  r  or  7T+Tr  ~  T+l- 


The  total  resistance  of  the  loop,  (x  +  r),  may  be  determined  by 
the  volt-ammeter  method. 

Formula  5  gives  the  resistance  in  ohms  from  the  sending 
end  to  the  fault.  If  the  conductors  are  both  of  the  same  mate- 
rial and  size  and  at  the  same  temperature,  the  resistance  per 
unit  length  will  be  the  same  for  both  and 

distance  to  fault  =  total  length  of  loop  X  (7  —  r  >  /  (6) 

V*r  ~T  J-x' 

The  resistance,  y,  from  the  far  end  of  the  line  to  the  fault  may 
also  be  obtained,  for 

7*  _r 

Ir~X 

or 

r  —  x 

Ix  -  Ir  _  r  -  x  _       2 
Ix  +  Ir  ~  r  +  x  ~  r  +  x 

2 

For  a  loop  of  uniform  resistance  per  unit  length, 
distance  from  far  end  of  line  to  fault  = 

length  of  one  wire  X    ^  --  /•  (7) 

1  x  T"  J-r 

The  two-ammeter  method,  using  alternating  currents,  has 
been  employed  by  Nicholson  to  locate  broken  or  otherwise  de- 
fective insulators  on  long  high-  voltage  transmission  lines.1  Few 
of  the  methods  of  fault  location  are  applicable  to  this  case,  for 
high  voltages  must  be  employed  in  order  that  the  defective 
insulator  may  arc  over  to  the  metal  supporting  pin  and  thus 
establish  the  fault.  Practically  full-line  voltage  may  be  required. 


678 


ELECTRICAL  MEASUREMENTS 


The  plant  where  this  method  was  first  tried  transmits  power  at 
60,000  volts,  25  cycles,  3-phase,  over  lines  160  miles  long.  The 
transformers  are  operated  with  a  grounded  neutral  and  the  insu- 
lator pins  are  grounded.  Consequently  if  an  insulator  breaks 
down  a  short-circuit  is  established  and  the  trouble  must  be 
rectified  before  service  can  be  resumed.  It  is  desirable  that 
special  apparatus  be  avoided. 

The  connections  are  shown  in  Fig.  420.  The  line  is  opened 
at  the  far  end  by  means  of  the  three  disconnecting  switches.  At 
the  near  end,  the  disconnecting  switches  in  A  and  B  are  opened 
and  jumpers  are  applied  at  both  ends  of  the  line  as  shown. 


FIG,  420. — Diagram  for  Nicholson's  application  of  the  two-ammeter  loop 
test  to  high-voltage  lines. 

At  R  is  a  rheostat  arrangement  to  control  the  current  after  the 
arc  to  ground  has  been  established;  F  is  an  expulsion  fuse  which 
short-circuits  R.  It  permits  the  voltage  at  the  fault  to  be  raised 
high  enough  to  start  the  arc  and  then  blows,  throwing  in  the 
controlling  resistance  R.  For  this  current-limiting  resistance  four 
concrete  columns  1  foot  square  and  12  feet  long  with  expanded 
metal  terminals  have  been  used.  Each  has  a  resistance  of  about 
2,000  ohms.  They  are  used  singly  or  in  parallel  as  occasion  re- 
quires. From  50  to  100  amperes  are  required  for  the  test.  In 
cases  where  the  striking  distance  is  several  inches,  the  testing 
current  does  not  burn  the  aluminum  conductors  if  it  is  kept  on  for 
40  seconds,  which  is  sufficient  time  to  obtain  the  readings. 

Where  a  single  size  of  conductor  is  employed,  it  is  found  that 
the  currents  divide  inversely  as  the  resistances  of  the  two  paths, 
so  formula  (6)  is  applicable. 

Murray  Loop  Test. — In  the  Murray  loop  test  the  connections 
are  such  that  the  resistances  x  and  r  form  two  arms  of  a  Wheat- 


CABLE  TESTING  679 

stone  bridge,  the  other  two  arms  being  made  up  of  resistances 
under  control  of  the  observer.  Fig.  421  shows  the  scheme  of 
connections. 

The  relative  positions  of  the  galvanometer  and  battery  are 
important;  with  the  connections  as  shown,  earth  currents  have 
no  effect  on  the  readings. 


]a                             b 

b 

FIG.  421. — Connections  for  Murray  loop  test  for  fault  location. 


When  the  galvanometer  stands  at  zero, 

M  _  r  M  +  N  _  r  -j-^x 

~N  ==  x    °r         N  x 


The  total  resistance  of  the  loop  (r  +  #)  is  obtained  by  a  bridge 
measurement. 

If  uniform  wires  are  being  dealt  with, 

/     N     \ 
distance  to  fault  =  total  length  of  the  loop  X  (  ™   .    ^)  • 

A  potential  divider  or  a  slide-wire  arrangement  with  extension 
coils  may  be  convenient  for  M  +  N,  in  which  case  M  +  N  is 
constant. 

A  cross  between  two  conductors  in  a  multiple-conductor  cable 
is  located  in  a  similar  manner,  the  only  difference  being  that  the 
battery,  instead  of  being  connected  to  ground,  is  attached  to  one 
of  two  faulty  conductors,  the  other  being  looped  with  an  unfaulted 
wire. 

Varley  Loop  Test. — In  this  method  a  fixed  bridge  ratio  is  used 
and  the  balance  obtained  by  adding  resistance  to  the  smaller 
section  of  the  loop  as  indicated  in  Fig.  422. 


680 


ELECTRICAL  MEASUREMENTS 


With  the  apparatus  arranged  as  in  Fig.  422  and  the  switch  in 
the  position  shown,  the  bridge  will  balance  when 

M  r 

N  "~  x  +  Pi 
PI  being  the  resistance  unplugged  at  P, 

(x  +  r)N  -  PiM 


or 


;-    x 


M  +  N 


(8) 


FIG.  422. — Connections  for  Varley  loop  test  for  fault  location. 

To  measure  (r  +  x),  the  total  resistance  of  the  loop,  the  key 
K  is  thrown  to  the  dotted  position  and  a  second  balance  obtained, 
using  the  apparatus  as  an  ordinary  Wheatstone  bridge. 

Determination  of  the  Total  Resistance  of  the  Defective  Con- 
ductor.— If  there  is  only  one  perfect  wire  between  the  stations, 
the  total  resistance  of  the  faulted  line  cannot  be  determined  by 
measurements  made  from  one  end  of  the  line. 


FIG.  423. — Pertaining  to  determination  of  resistance  of  faulty  conductor. 

The  determination  may  be  made  by  tests  from  both  ends. 
The  line  is  first  looped  with  Z  at  B  and  x  determined  by  one  of 
the  previous  methods.  Then  the  loop  is  made  at  A  and  the 
observer  at  B  measures  y.  The  total  resistance  is  obviously 
(x  +  y).  (See  Fig.  423.) 

When  there  are  two  perfect  wires  between  the  stations, 
measurements  from  one  end  of  the  line  suffice.  When  dealing 
with  a  multiple-conductor  cable,  two  unfaulted  wires  in  the  same 
cable  may  be  used  as  the  auxiliary  wires  (see  Fig  424). 


CABLE  TESTING  681 

The  faulty  wire  is  looped  with  Z  and  the  resistance,  Rj}  of 
the  loop  measured  by  a  bridge. 

•  Ri  =  (x  +  y)  +  Z. 

Loop  the  faulty  wire  with  W  and  measure  the  resistance,  Rz, 
of  this  loop. 

Rz  =  (x  +  y)  +  W. 


w 


7 


r * — 4—     —  y -1 

w& 

FIG.  424. — Pertaining  to  determination  of  resistance  of  faulty  conductor. 

Lastly,  loop  W  and  Z  and  measure  the  resistance,  R3,  of  the 
loop. 

R.  =  W  +  Z. 
Then 

,  .         RI  -\-  Rz  —  Rs  /r.x 

(a;  +  2/)  =  -       —3-  (9) 

Another  procedure  is  to  loop  the  faulty  wire  with  Z  and 
measure  the  loop  resistance,  Ri. 

Ri  =  (x  +  y)  +  Z. 

W  and  Z  are  then  looped  and  grounded  at  B,  and  Z  measured 
by  one  of  the  previous  methods;  then 

{x  +  y)  =  Ri  -  Z  (10) 


w 


± 


FIG.  425. — Pertaining  to  determination  of  resistance  of  faulty  conductor. 

If  there  are  one  perfect  and  two  faulty  wires  of  the  same  length 
and  resistance  connecting  the  stations,  as  indicated  in  Fig.  425, 
the  total  resistance  of  either  of  the  faulty  wires  may  be  obtained 
thus: 


682 


ELECTRICAL  MEASUREMENTS 


Loop  Z  and  W  and  measure  the  resistance,  RI,  of  the  loop. 
Loop  (x  4-  y)  and  W  and  measure  the  resistance,  RI,  of  this  loop. 
Finally,  connect  Z  and  (x  +  i/)  in  parallel  and  loop  the  combina- 
tion with  W  and  measure  the  resistance,  R^. 

Ri  =  Z  4-  W. 

R*  =  (x  4-  y)  4-  Tf . 


Or, 


-  R,)        (11) 


Z/  7D  T)    \        |        A  /  /  D  H>    "\     /  D  D    \ 

=   (ill  —  tt&)     i      v  ^«j  —  Kz)  (a>t  —  *•!/• 

To  be  strictly  accurate,  the  ratio  of  the  resistance  up  to 
the  fault  to  the  total  resistance  of  the  wire  should  be  the  same 
for  both  defective  conductors,  for  then  there  will  be  no  flow  of 
current  through  the  faults. 


-w- 


W- 


M' 


N' 


FIG.  426. — Connections  for  Fisher  loop  test  for  fault  location. 

Fisher  Loop  Test. — In  order  to  make  this  test  there  must  be 
two  unfaulted  wires  which  run  from  the  testing  station  to  the 
far  end  of  the  line.  The  result  obtained  is  the  same  as  that  given 
by  the  above  methods  where  two  perfect  conductors  are  available 
and  both  the  resistance  up  to  the  fault  and  the  total  resistance 
of  the  faulty  line  are  measured. 


CABLE  TESTING                                683 

Two  balancings  are  necessary,  as  indicated  in  Fig.  426. 
From  the  first  balancing, 

M  Z  +  y 

W  :  x 

From  the  second  balancing, 

M'  Z 


Nr      x  -+-  y 
Then 


N' 


(12) 


If  a  slide  wire  or  its  equivalent  is  used  for  the  balance  arms, 
M  +  N  =  M'  +  N'  and 

x  =  (x  +  y)"™  (12a) 

When  the  resistance  per  unit  length  of  conductor  is  uniform, 

|r'         \ 
F7+   1 
^Tf—      1  X  (length  of  cable)        (13) 


Corrections  for  Conductors  of  Different  Diameters.  —  In  the 

foregoing  it  has  been  assumed  that  the  resistance  per  unit  length 
of  cable  is  uniform.  In  some  cases,  however,  the  conductor  may 
be  made  up  of  a  number  of  wires  in  series  which  have  different 


£-iA ^ ^J 


T# 

FIG.  427. — Pertaining    to    the    location    of    a   ground   in    a   non-uniform 

conductor. 

diameters.  The  lengths  and  sizes  of  the  wires  in  the  different 
sections  will  be  known  from  the  office  records.  Let  the  lengths 
be  h,  Z2,  h,  .  .  .  and  let  the  corresponding  resistances  per  unit 
length  be  Kit  K2,  K^  .  .  .  The  resistances  of  the  sections  will 
be  as  indicated  in  Fig.  427. 


684  ELECTRICAL  MEASUREMENTS 

To  locate  the  section  in  which  the  fault  exists,  compare  the 
resistance  x  as  found  by  one  of  the  previous  methods,  with  l\K\, 
then  with  l\K±  +  Z2K2  and  so  on.  Suppose  that  the  comparison 
shows  the  fault  to  be  in  the  third  section;  then 

x  =  hK,  +  IzK*  +  l',K3 

and  the  distance  of  the  fault  beyond  the  junction  of  the  second 
and  third  sections  is 


Uncertainty  as  to  the  values  of  K  introduces  difficulties.  The 
average  values  of  K  for  the  different  sections  depend  on  the 
diameters  of  the  wires,  their  conductivities,  the  temperatures  of 
the  sections,  and  in  underground  conductors  of  'large  cross- 
section,  where  the  lengths  of  the  sections  are  short,  on  the 
number  of  joints. 

In  cables  for  large  currents  laid  in  ducts  where  the  temperatures 
may  be  high,  there  may  be  great  uncertainty  as  to  the  tem- 
perature and  a  consequent  difficulty  in  correcting  K\,  Kz,  etc., 
to  obtain  their  values  at  the  time  of  test. 

Locating  Faults  in  Underground  High-tension  Cables.2  —  In 
locating  faults  in  underground  high-tension  cables,  special 
difficulties  are  experienced  because  of  the  low  resistance  of  the 
conductor,  which  may  be  from  0.10  to  0.04  ohm  per  1,000  feet. 
On  the  other  hand,  such  cables  are  readily  accessible  at  the  man- 
holes, which  may  be  about  300  feet  apart.  This  makes  it  possible, 
before  cutting  the  cable,  to  verify  the  location  of  the  fault  as 
given  by  a  loop  test,  and  for  this  purpose  special  apparatus  has 
been  devised  so  that  the  particular  length  of  cable  in  which  the 
fault  is  located  may  be  identified  with  certainty.  This  verifica- 
tion is  necessary,  for  in  a  10-mile  length  of  cable  an  uncertainty 
of  0.3  per  cent  in  the  resistance  measurements  corresponds  to 
an  uncertainty  of  158  feet  or  half  a  length  of  the  cable  between 
manholes. 

In  the  long  run,  time  will  be  saved  by  adopting  an  orderly 
procedure  and  the  following  has  been  found  satisfactory  in  dealing 
with  this  class  of  faults  :  2 

(A)  Tests  to  diagnose  the  trouble  and  show  the  tester  what 
he  has  to  deal  with. 


CABLE  TESTING  685 

(B)  Reduction  of  the  resistance  of  the  fault   (if  necessary) 
so  that  current  sufficient  to  make  the  location  and  verification 
tests  will  flow  through  the  fault  with  a  moderate  voltage. 

(C)  Preliminary  location  of  the  fault  by  a  loop  test.     If  the 
conductor  is  burned  off  the  loop  test  is  not  applicable.     In 
this  case  the  ground  is  located  by  use  of  an  exploring  coil,  see 
D  below. 

(D)  Verification  of  the  location  by  use  of  an  exploring  coil. 
(A)   Taking  a  three-phase  cable: 

1.  All  three  conductors  are  insulated  at  both  ends  and  the 
resistance  to  ground  of  each  conductor  determined  by  the  volt- 
meter method,  using  a  direct-current  potential  of  about  110 
volts.     This  shows  whether  the  fault  is  a  ground  or  not  and  if  it 
is,  gives  an  idea  of  the  fault  resistance. 

2.  If  a  low-resistance  ground  is  found,  verify  No.  1  by  using 
a  test  lamp,  that  is,  an  incandescent  lamp  with  one  side  of  the 
socket  attached  to  the  110-volt  direct-current  supply,  the  other 
being  provided  with  a  flexible  cord  so  that  it  may  be  attached  to 
any  of  the  conductors.     If  the  lamp  glows,  the  resistance  of  the 
fault  is  to  be  measured  by  a  bridge,  two  readings,  with  reversed 
currents,  being  taken.     This  measurement  of  the  fault  resist- 
ance shows  whether  it  is  necessary  to  further  reduce  it  before 
making  the  loop  and  verification  tests. 

3.  Conductors  which  show  the  same  insulation  to  ground  should 
now  be  tested  to  determine  whether  this  is  due  to  the  wires  being 
crossed.     The  test  is  made  by  grounding  one  of  the  wires  and 
remeasuring  the  resistance  to  ground  of  the  others.     If  the  volt- 
meter method  shows  that  this  resistance  is  low,  it  should,  for  the 
reason  stated  in  2,  be  measured  by  the  bridge. 

4.  The  far  ends  of  all  three  conductors  should  be  carefully 
connected  together  and  the  resistances  of  all  the  uncrossed  loops 
measured  by  the  bridge.     A  comparison  of  these  results  with  the 
resistances  computed  from  the  known  size  and  length  of  the  line 
will  show  if  there  are  open  faults;  that  is,  places  where  the  wires 
are  broken  or  burned  off.     If  an  open  fault  exists,  an  idea  of  its 
resistance  should  be  obtained.     The  resistance  to  ground  of  the 
near  side  of  the  open  fault  has  been  obtained  in  No.  1.     The 
resistance  to  ground  of  the  far  side  of  the  open  fault  is  obtained 
by  measuring  it  via  an  unfaulted  conductor,  which  is  used  as  a 


686  ELECTRICAL  MEASUREMENTS 

lead.  If  this  resistance  is  very  low,  the  resistance  across  the  open 
fault  has  practically  been  measured  in  No.  1.  If  it  is  not  low,  it 
should  be  determined  by  measuring  the  insulation  of  the  open 
phase  when  the  far  side  is  grounded  through  one  of  the  unfaulted 
conductors. 

(B)  In  order  to  locate  the  ground,  it  is  necessary  that  the  fault 
resistance  be  low,  so  that  sufficient  current  for  the  tests  may  be 
obtained  with  low  voltage.     This  is  convenient  in  the  loop  tests 
and  is  necessary  in  the  subsequent  exact  localization  by  means 
of  exploring   coils.     For,   if   considerable   voltage   is   used,  the 
charging  current  going  to  the   parts  of  the  cable   beyond  the 
fault  produces  confusion  and  renders  the  localization  a  matter  of 
difficulty. 

After  having  determined  the  nature  of  the  fault  and  gained 
an  idea  of  its  resistance,  it  will  probably  be  found  necessary  to 
reduce  the  fault  resistance.  The  fundamental  idea  is  to  carbon- 
ize a  sufficient  amount  of  the  paper  insulation  at  the  fault,  so 
that  a  current  of  1  or  2  amperes  may  be  carried  for  several  hours. 
Practice  is  required  to  acco'mplish  this  in  the  shortest  possible 
time  and  without  any  approach  to  an  explosive  short-circuit  at 
the  fault,  which  would  destroy  the  continuity  of  the  path  via 
the  carbonized  paper.  When  the  fault  is  not  submerged  in 
water,  for  in  water  the  paper  cannot  be  carbonized,  the  procedure 
is  to  send  a  current  of  from  3  to  5  amperes  through  the  fault  for  10 
minutes,  in  order  to  dry  it  out,  and  to  follow  this  by  a  current  of 
about  1  ampere,  for  5  minutes,  to  carbonize  the  paper.  High- 
resistance  faults  at  a  considerable  distance  from  the  testing  station 
give  trouble  on  account  of  the  charging  current.  In  such  cases, 
the  current  through  the  fault  may  be  determined  by  aid  of  a 
wattmeter. 

(C)  After  having  reduced  the  fault  resistance,  a  Murray  01  a 
Varley  loop  test  is  used  to  determine  the  approximate  location 
of  the  trouble. 

In  making  this  test,  great  care  must  be  exercised  in  applying 
the  jumpers  at  the  far  end  and  in  joining  the  bridge  to  the  cable, 
in  order  that  extraneous  resistances  may  not  be  introduced. 
Also  allowance  must  be  made  for  the  leads  connecting  the  bridge 
to  the  cable  or  else  the  bridge  must  be  so  constructed  that  these 
resistances  are  eliminated. 


CABLE  TESTING  687 

Irregularities  in  joint  resistances,  etc.,  render  it  necessary  to 
supplement  the  loop  tests  by  exploration  tests  which  will  show 
definitely  the  particular  length  of  cable  in  which  the  fault  exists. 
Also  the  cable  may  be  burned  off,  in  which  case  the  loop  tests 
are  not  applicable. 

(D)  The  idea  of  the  exploration  tests  is  to  send  some  char- 
acteristic signal  into  the  cable  and  to  find  by  means  of  a  suitable 
detector  the  point  at  which  the  signal  ceases  to  be  heard  as  the 
exploring  device  is  moved  along  the  cable. 

Taking  the  case  shown  in  Fig.  428,  when  the  sheaths  of  the 
various  lengths  of  cable  are  bonded,  to  prevent  electrolysis,  a 


FIG.  428. — Pertainirlg  to  locating  a  ground  by  exploration  tests. 

diminishing  portion  of  the  current  will  flow  in  the  sheath  to 
points  beyond  the  ground,  as  indicated.  Currents  will  also  flow 
in  the  sheath,  which  are  due  to  inequalities  of  ground  potential, 
as  produced,  for  example,  by  stray  currents  from  street-car  lines. 

If  the  detector  is  a  simple  coil  of  wire  connected  to  a  telephone 
and  held  with  its  plane  parallel  to  the  length  of  the  cable,  the 
sheath  currents,  from  whatever  cause,  will  affect  it  in  the  same 
manner  as  if  they  flowed  in  the  conductor  and  an  exact  location 
of  the  trouble  is  not  possible. 

When  dealing  with  three-phase  cables,  it  is  possible  to  use  a 
longitudinal  exploring  coil,  devised  by  W.  A.  Durgin,  which  is 
not  affected  by  the  sheath  currents. 

It  depends  for  its  effectiveness  on  the  fact  that  the  conductors 
in  the  cable  are  spiralled,  the  lay,  or  length  of  a  complete  spiral, 
being  about  20  inches,  for  a  No.  2-0  three-phase  paper-insulated 
cable. 

The  exploring  coil  consists  of  a  laminated  iron  core,  of  a  length 
determined  by  the  lav  of  the  cable,  over  which  is  wound  a  coil  of 
insulated  wire  with  its  terminals  attached  to  a  telephone.  The 
core  is  placed  parallel  to  the  axis  of  the  cable.  Any  current 


688 


ELECTRICAL  MEASUREMENTS 


which  flows  only  in  the  sheath  produces  a  field  which  has  no 
longitudinal  component  and,  therefore,  stray  currents  cause  no 
disturbance  of  the  telephone. 

Referring  to  Fig.  429,  when  a  current  flows  out  along  the  spi- 


Sheath 

FIG.  429. — Diagram  for  Durgin  exploring  coil. 

railed  conductor  ab  and  returns  along  the  sheath,  in  effect  along 
cd,  the  case  is  entirely  different  for  there  is  a  loop  twisted  so  that 
it  alternately  presents  its  positive  and  negative  side  to  the  obser- 
ver as  he  passes  along  an  element  of  the  sheath;  that  is,  positions 

of  maximum  and  minimum  magnetic 
potential  .succeed  each  other  in  a 
definite  order. 

When  the  longitudinal  exploring 
coil  is  used  in  the  case  shown  in  Fig. 
428,  it  will  be  found  that  no  indica- 
tion is  obtained  at  points  near  the 
signalling  apparatus,  for  at  these 
points  there  is  little  return  current  in 
the  sheath  and  the  effect  of  a  twisted 
loop  is  not  obtained.  On  approach- 
ing the  ground,  more  and  more  cur- 
rent flows  in  the  sheath  and  the 
signals  increase  in  intensity  until  the 
ground  is  reached;  beyond  this  point 
there  is  silence,  for  only  sheath  cur- 
rents are  present  and  they  produce 
no  longitudinal  field. 

Another  use  of  the  exploring  coil  is 
in  identifying  a  particular  cable  in 
the  distributing  system.  When  deal- 
ing with  three-phase  cables,  there  are  three  signalling  loops 
which  may  be  utilized. 

I.  Two  conductors,  the  current  flowing  out  by  one  and  return- 
ing by  the  other. 


FIG.  430. — Showing  mag- 
netic equipotential  lines 
around  a  three-phase  cable 
when  steady  current  flows  in 
the  signalling  loop  formed  by 
conductors  A  and  B. 


CABLE  TESTING 


689 


II.  Two  conductors  in  parallel  and  in  series  with  the  third. 

III.  One  conductor  and  the  sheath. 

For  purposes  of  explanation  take  the  first  case;  the  equipoten- 
tial  lines  on  a  plane  perpendicular  to  the  axis  of  the  cable,  and 
due  to  a  steady  current,  are  shown  in  Fig.  430. 

It  is  evident  that  because  of  the  position  of  the  conductors  in 
the  cable,  the  magnetic  potential  varies  from  point  to  point 
around  the  circumference  of  the  sheath  and  that  the  maximum 
and  minimum  points  are  180°  apart.  This  means,  that  on  ac- 
count of  the  lay  of  the  cable,  the  distance  between  the  points  of 
the  maximum  and  minimum  magnetic  potential  when  measured 
along  an  element  of  the  sheath  is  one-half  the  lay  of  the  cable. 
If  the  iron  core  of  the  exploring  coil  has  a  length  equal  to  one- 
half  the  lay  and  is  applied  longitudinally  to  the  cable  between 
these  points,  it  will  be  traversed  by  a  considerable  flux,  and  a 
signal  sent  into  the  cable  will  be  audible  in  the  telephone.  Sheath 
currents  of  any  sort  are  not  effective  in  producing  sounds  in  the 
telephone  for  they  cause  no  inequalities  of  magnetic  potential 
along  the  length  of  the  cable. 


£ 

SI 

33 


in 


\ 


50 
Percent  of  Lay 


100 


FIG.  431. — Showing   variation   of   magnetic   potential   when    different 
signalling  loops  are  used. 

The  two-conductor  circuit,  I,  is  best  when  a  cable  has  to  be 
identified  throughout  its  length  because  it  gives  the  maximum 
difference  of  magnetic  potential  and  also  because  the  maximum 
and  minimum  points  are  equally  spaced. 

With  connection  II,  the  maximum  and  minimum  points  are 
spaced  alternately  40  per  cent  and  60  per  cent  of  the  lay. 

44 


690 


ELECTRICAL  MEASUREMENTS 


With  III,  the  corresponding  spacing  is  35  and  65  per  cent  of 
the  lay  (see  Fig.  431.) 

When  locating  high-resistance  grounds,  all  the  conductors 
are  connected  in  parallel  so  that  the  charging  current  to  the  por- 
tion of  the  cable  beyond  the  fault  may  not  produce  a  sound  in  the 
telephone.  To  send  the  characteristic  signal  into  the  cable,  a 
motor-driven  commutator  is  used  which  will  break  the  circuit 
about  3,000  times  per  minute;  in  series  with  it-is  a  make-and- 
break  switch  actuated  by  a  cam  also  driven  by  the  motor.  The 
result  is  that  one  hears  in  the  telephone  a  definite  note  which  is 
interrupted  in  some  particular  manner. 

Location  of  Total  Disconnection. — A  total  disconnection  occurs 
when  the  wire  breaks  inside  the  insulating  covering  and  the  ends 
are  pulled  so  far  apart  that  the  two  sections  of  the  conductor 
are  insulated  from  each  other. 

Theoretically,  the  conductors  in  a  cable  occupy  definite  posi- 
tions with  respect  to  each  other  and  to  the  sheath.  This  being 
so,  the  electrostatic  capacity  measured  between  two  conductors 
or  between  a  conductor  and  sheath  should  be  proportional  to 


h- 1 


FIG.  432. — Connections  for  direct  deflection  method  for  measuring  electro- 
static capacity  of  cable. 

the  length  of  the  cable.  Consequently,  when  the  insulation 
remains  intact,  it  should  be  possible  to  locate  a  total  disconnec- 
tion by  measuring  the  electrostatic  capacity  of  the  portion  of  the 
cable  from  the  testing  station  up  to  the  break  and  comparing  it 
with  the  capacity  of  the  whole  cable.  If  the  total  capacity  is  not 
known,  measurements  must  be  made  from  both  ends  of  the  line. 
The  capacities  may  be  measured  by  the  direct  deflection 
method,  the  connections  for  which  are  shown  in  Fig.  432.  Some 


CABLE  TESTING  691 

definite  procedure  should  be  adopted  and  used  throughout  the 
test,  in  order  that  the  effects  of  absorption  may  be  eliminated. 

The  ballistic  deflection  of  the  galvanometer  which  occurs  when 
the  key,  Kz,  is  thrown  to  the  right,  is  read  and  compared  with  the 
ballistic  deflection  obtained  when  the  standard  condenser  is 
substituted  for  the  cable,  the  battery  being  kept  constant.  It- 
may  be  necessary  to  change  the  effective  sensitivity  of  the  gal- 
vanometer, consequently  an  Aryton  shunt  may  be  used,  as  sug- 
gested by  the  Fig.  432.  The  lead  from  the  key  to  the  cable  core 
should  be  as  short  as  possible.  If  necessary,  its  capacity  may 
be  determined  and  a  suitable  correction  made. 

The  capacity  may  also  be  measured  by  the  simple  bridge 
method  (see  page  392).  The  connections  for  a  single-conductor 
cable  or  its  equivalent  are  shown  in  Fig.  433. 


Generator 

G.r.o.und  01  UnfauJted  Conductor 

FIG.  433. — Simple  bridge  method  for  measuring  electrostatic  capacity  of  a 
short  length  of  cable. 

In  this  case  it  is  convenient  to  use  an  alternating  current  or  a 
rapidly  interrupted  direct  current  and  to  employ  a  telephone  as 

M 

the  detector.     When  the  ratio    ^   has  been  adjusted  so  that 

M       Cx 
there  is  the  minimum  sound  in  the  telephone,   ,,.   =  „*- 

or 

C    =  C      • 

N 

The  capacity  of  the    other  section,   CV1  may  be  similarly  de- 
termined by  tests  from  the  far  end  of  the  line. 
Then: 

/     Cx     \ 

Distance  to  the  fault  =  total  length  of  cable  (^   _J^  ) 

The  condensers  used  for  Cs  should  be  of  good  quality  and  the 
procedure  adopted  should  be  the  same  as  that  employed  when 
their  capacities  were  measured. 


692  ELECTRICAL  MEASUREMENTS 

Where  there  are  several  pairs  of  wires  in  the  cable,  a  pair 
may  sometimes  be  used  in  place  of  the  standard  condenser,  as 
indicated  in  Fig.  434. 


Length    x 


Generator 

FIG.  434. — Bridge  measurement  of  capacity  to  total  disconnection;  using 
the  capacity  of  an  unfaulted  pair  as  a  standard. 


In  this  case,  from  the  construction  of  the  cable,  the  capacity 
per  unit  length  for  both  pairs  is  nominally  the  same,  and  as 

M_  C, 

N  ''=  Cs' 

distance  to  the  fault  =  total  length  of  cable  X  (jr) .       (16) 

These  methods  of  location  by  capacity  measurements  are  con- 
venient when  dealing  with  telephone  cables.  The  difficulty  in 
applying  them  to  power  cables  is  that  the  disconnection,  due  to 
a  burn-out,  may  not  be  total  and  that  the  apparent  capacity 
per  unit  length  may  not  be  uniform. 

Breakdown  Tests  of  High-voltage  Cables. — In  addition  to 
the  tests  which  are  made  during  the  process  of  manufacture, 
every  high- voltage  cable  must  be  subjected  to  a  breakdown  test 
after  it  has  been  installed  and  before  it  is  accepted,  the  object 
being  to  search  out  the  weak  spots  due  to  defects  of  manufacture 
and  of  installation,  especially  defects  at  the  joints. 

In  this  connection  it  may  be  pointed  out  that  laboratory  tests 
on  short  samples  show  higher  breakdown  voltages  than  are 
realized  in  practice  and  are  without  value  as  indicating  what 
may  be  expected  of  long  lengths  of  cable. 

The  idea  of  the  breakdown  test  is  simple.  A  specified  voltage 
is  applied  between  conductors,  or  between  conductors  and  sheath, 
for  a  specified  time.  If  a  breakdown  occurs,  the  fault  is  located 
by  one  of  the  methods  already  described,  the  cable  is  patched  and 


CABLE  TESTING  693 

the  test  repeated.     A  frequency  of  25  cycles  per  second  is  com- 
monly employed  in  these  tests. 

In  the  practical  execution  of  breakdown  tests,  numerous 
questions  arise,  such  as: 

1.  Given  the  size  of  wire,  thickness  of  insulation  and  the 
character  of  the  insulating  material,  what  test  voltage  should 
be  applied? 

2.  For  how  long  a  time  should  the  test  voltage  be  maintained? 

3.  How  can  the  wave  form  of  the  test  voltage  be  assured? 

4.  How  shall  the  voltage  be  measured  so  that  the  maximum 
stress    to    which   the   insulation    is    being    subjected    may    be 
known? 

5.  What  precautions  must  be  taken  in  order  that  high-frequency 
disturbances  set  up  by  spark  discharges  from  the  testing  circuits 
may  be  eliminated?     The  cable  breakdown  may  be  due  to  the 
high-frequency    disturbance    rather   than    to    the    regular   test 
voltage,  so  the  observer  is  misled. 

6.  Is  it  possible  to  determine  whether  or  not  a  cable,  which 
has  not  been  actually  broken  down,  has  been  overstressed  by  the 
high-voltage  test  so  that  it  is  permanently  injured? 

Though  breakdown  tests  are  of  the  highest  importance  to 
operating  companies,  up  to  the  present  time  no  generally  ac- 
cepted procedure  has  been  developed. 

A  high  test  voltage  is  advisable  since  it  promotes  care  on  the 
part  of  the  manufacturer;  on  the  other  hand,  it  is  possible  to  so 
overstress  a  cable,  without  actually  breaking  it  down,  that  it  is 
permanently  injured  and  may  in  consequence  fail  at  some 
future  time  when  conditions  are  not  abnormal. 

In  the  past,  many  companies  have  specified  that  the  cable 
must  stand  2J^  times  the  normal  working  voltage  for  5  minutes, 
but  there  is  no  rational  basis  for  this  particular  requirement. 

At  the  present  time,  on  account  of  the  lack  of  necessary  data, 
it  is  not  possible  to  specify  the  proper  test  voltage  from  the 
dimensions  and  properties  of  the  insulation. 

A  great  difficulty  in  applying  mathematical  analysis  to  this 
problem  arises  from  the  non-uniformity  of  the  insulating  materials. 
Air  pockets  in  the  dielectric  and  lack  of  perfect  adherence  of  the 
dielectric  to  the  conductor,  especially  in  stranded  cables,  produce 
local  overstressing  and  deterioration  of  the  insulation  under 


694 


ELECTRICAL  MEASUREMENTS 


prolonged  application  of  voltage,  and  are  factors  which  cannot  be 
taken  into  account  in  the  analysis. 

Paragraph  684  of  the  Standardization  Rules  of  the  American 
Institute  of  Electrical  Engineers,  1916,  is  as  follows: 

"The  following  test  voltages  shall  apply  unless  a  departure  is  con- 
sidered necessary,  in  view  of  the  above  circumstances.  Rubber-covered 
wires  or  cable  for  voltages  up  to  7  kv.  shall  be  tested  in  accordance  with 
the  National  Electric  Code.  Standardization  for  higher  voltages  for 
rubber-insulated  cables  is  not  considered  possible  at  the  present  time. 

"  Varnished  cambric  and  impregnated  paper  insulated  wires  or  cables 
shall  be  tested  at  the  place  of  manufacture  for  five  (5)  minutes  in 
accordance  with  the  Table  XIV  below. 

TABLE  XIV. — RECOMMENDED  TEST  KILOVOLTS  CORRESPONDING  TO  OPERAT- 
ING KILOVOLTS 


Operating  kv. 

Test  kv. 

Operating  kv. 

Test  kv. 

Below  0.5 

2.5* 

5 

14 

0.5 

3.0 

10 

25 

1.0 

4.0 

15 

35 

2.0         x 

6.5 

20 

44 

3.0 

9.0 

25 

53 

4.0 

11.5 

• 

"  Different  engineers  specify  different  thickness  of  insulation  for  the 
same  working  voltages.  Therefore,  at  the  present  time  the  test  kv. 
corresponding  to  working  kv.  given  in  Table  XIV  are  based  on  the 
minimum  thickness  of  insulation  specified  by  engineers  and  operating 
companies. "f 

*The  minimum  thickness  of  insulation  shall  be  ^Q  in.  (1.6  mm.). 

f  The  Standards  Committee  does  not  commit  itself  to  the  principle  of  bas- 
ing test  voltages  on  working  voltages,  but  it  is  not  yet  in  possession  of  suffi- 
cient data  to  base,  them  upon  the  dimensions  and  physical  properties  of  the 
insulation. 

When  testing  insulations  for  dielectric  strength,  it  is  essential 
to  employ  a  generator  which  under  all  conditions  gives  practically 
a  sinusoidal  voltage  at  the  specimen,  since  the  maximum  stress 
to  which  the  insulation  is  subjected  should  be  known.  For 
example,  altering  the  length  of  cable  under  test,  that  is,  changing 
the  electrostatic  capacity  placed  across  the  secondary  terminals 
of  the  testing  transformer  must  not  deform  the  wave.  The  wave 


CABLE  TESTING  605 

form  must  also  be  independent  of  the  particular  combination  of 
transformer  windings  which  are  used  to  obtain  the  required 
voltage  and  must  be  uninfluenced  by  the  method  of  voltage  regu- 
lation. The  instruments  commonly  used  for  measuring  the 
voltage,  i.e.,  electrostatic  voltmeters  and  electrodynamometer 
voltmeters,  give  the  effective  or  r.m.s.  value  of  the  voltage. 
If  the  wave  is  sinusoidal,  the  maximum  value  is  obtained  by 
multiplying  the  effective  value  by  \/2. 

If  the  voltage  wave  is  not  sinusoidal,  resonance  effects  due  to 
the  capacity  of  the  cable  and  the  reactance  of  the  apparatus 
may  be  present,  so  that  from  this  cause  the  wave  may  be  distorted 
in  a  manner  dependent  on  the  length  of  the  cable  under  test. 

The  effect  resulting  from  taking  the  insulation  through  cycles 
of  electrostatic  stress  depends  not  only  on  the  maximum  voltage 
but  on  the  number  of  times  the  cycle  is  repeated  in  a  second. 
If  the  voltage  wave  be  very  greatly  distorted,  this  effect  and  the 
consequent  weakening  of  the  dielectric  strength  of  the  cable  due 
to  a  prolonged  application  of  the  test  voltage,  are  abnormal  and 
the  results  will  not  be  comparable  with  those  obtained  with  a 
very  different  wave  form. 

The  following  series  of  oscillograms  serve  to  show  the  neces- 
sity for  the  proper  equipment  when  dielectric  strengths  are  to 
be  measured.3  The  generator  used  in  the  tests  was  a  motor- 
driven,  25-kva,  220-volt,  4-pole,  25-cycle,  single-phase  alternator, 
having  10  slots  per  pole  and  a  conductor  belt  five-eighths  the 
pole  pitch.  The  transformer  capacity  was  50  kva.,  220-50,000 
volts.  The  secondary  consisted  of  four  separate  12,500-volt 
coils.  The  high-tension  winding  had  a  total  of  12,512  turns;  the 
low-tension  55  turns.  The  reactance  voltage  was  about  6  per 
cent.  This  transformer  was  operated  at  high  saturation. 

Fig.  435  shows  that  the  e.m.f.  of  the  generator  is  nearly  enough 
sinusoidal  and  if  the  wave  form  could  be  maintained,  satisfactory 
tests  would  be  possible.  .  Fig.  436  shows  the  result  when  the 
transformer,  with  the  secondary  circuit  open,  is  attached  to  the 
generator.  The  exciting  current  is  much  distorted  owing  to  the 
changes  of  permeability  incident  to  working  the  core  at  high 
saturation,  and  a  small  third  harmonic  appears  in  the  P.D.  wave. 

A  cable  having  a  capacity  of  0.13  microfarad  was  attached  to 
the  secondary.  Such  a  load  will  take  a  large  leading  current 


696 


ELECTRICAL  MEASUREMENTS 


and  cause  great  modification  of  the  voltage  wave  form.  Using 
all  the  secondary  coils  in  series,  the  50,000-volt  connection,  the 
results  shown  in  Fig.  437  were  obtained.  Fig.  438  shows  the 


FIG.  435. — Open-circuit  voltage  of  generator. 


FIG.  436. — P.D.  and  exciting-current  waves,  transformer  only. 


FIG.  437. — P.D.  and  exciting-current  waves  when  cable  having  a  capacity  of 
0.13  M.F.  is  attached  to  transformer;  50,000-volt  connection  used. 

results  when  the  secondary  coils  were  used,  two  in  series  and  two 
in  parallel,  the  25,000-volt  connection. 

When  the  change  was  made  from  the  50,000  to  the  25,000-volt 


CABLE  TESTING 


697 


connection,  the  generator  voltage  was  practically  doubled  so 
that  the  effective  voltage  at  the  cable  was  the  same  in  both 
cases. 

It  is  seen  that  with  the  same  generator,  the  same  transformer, 
the  same  frequency  and  the  same  cable  an  approximately  sinu- 
soidal P.D.  wave  becomes  badly  distorted  by  simply  changing 
the  transformer  ratio  and  the  generator  voltage. 

These  effects  may  be  explained  in  a  general  way  as  follows: 
As  the  generator  is  a  single-phase  machine,  the  tendency  of  the 
armature  reaction  is  to  introduce  a  third  harmonic  in  the  P.D. 
wave.  The  transformer  is  worked  at  high  saturation  and  through 


FIG.  438. — P.D.  and  exciting  current  waves  when  cable  having  a  capacity 
of  0.13  M.F.  is  attached  to  transformer;  25,000-volt  connection  used. 

variations  in  the  permeability  of  the  core  introduces  harmonics, 
especially  the  third,  into  the  magnetizing  current.  These  har- 
monics appear  in  the  voltage  wave  and  are  intensified  by  the 
capacity  load  on  the  secondary  of  the  transformer. 

In  addition,  resonance  effects  are  probably  present.  Attempts 
at  tuning  the  circuit  by  an  iron-cored  reactance  in  parallel  with 
the  transformer  were  not  successful,  for: 

1.  The  minimum  current  does  not  necessarily  correspond  to 
the  best  wave  form. 

2.  The  best  wave  form  may  occur  at  an  abnormally  large 
value  of  lagging  current. 

3.  The  wave  form  cannot  be  made  sinusoidal  in  every  case. 


698 


ELECTRICAL  MEASUREMENTS 


It  is  obvious  that  a  different  design  of  generator  and  trans- 
former must  be  used. 

To  preserve  a  sinusoidal  wave  form,  the  generator  should  be 
a  F-wound  three-phase  machine  with  non-salient  poles;  it  should 
have  a  distributed,  fractional-pitch  (%)  winding  and  be  provided 
with  damping  grids. 

The  use  of  the  F-wound  three-phase  machine  eliminates  the 
third  harmonic  in  the  e.m.f.  wave;  the  fractional  pitch  greatly 
reduces  the  fifth  and  seventh  harmonics  and  the  damping  grids 
tend  to  damp  single-phase  pulsating  armature  reaction. 

The  transformer  should  be  designed  to  work  at  low  saturation. 

Tests  of  such  a  machine  and  transformer  (designed  by  C.  A. 
Adams)  fail  to  show  any  appreciable  distortion  of  the  wave  form 
under  the  most  exacting  conditions.  No  testing  set  should  be 
installed  which  is  incapable  of  maintaining  a  sinusoidal  test 
voltage  under  all  circumstances.  Questions  as  to  peak  voltages 
and  abnormal  dielectric  losses  are  thus  eliminated. 

Measurement  of  Peak  Voltage. — Those  interested  in  the  pur- 
chase and  installation  of  cables  should  be  able  to  satisfy  them- 


Air  Condeaser 

nnrl 


Choke  Coil 


Synchronous 
Contactor 


.y 

otentiometer^ 


FIG.  439. — Chubb  and   Fortescue   arrangement  for   measuring   high 
peak-voltages. 

selves  as  to  the  maximum  voltage  applied  to  the  cable  during 
the  breakdown  test,  for  as  shown  by  the  above  oscillograms  it 
may  happen  that  the  effective  value  of  the  voltage  may  give 
little  information  as  to  its  peak  or  maximum  value.  Also  inter- 
ested parties  may  be  skeptical  as  to  the  maintenance  of  the  sinu- 
soidal wave  form,  even  when  the  proper  testing  equipment  is 
used,  and  hence  must  be  satisfied. 


CABLE  TESTING  699 

The  spark-gap  method  of  measuring  peak  voltages  referred 
to  on  page  260,  is  not  directly  applicable  in  cable  testing,  for 
the  observer  should  be  able  to  follow  the  variation  of  the  voltage. 

Chubb  and  Fortescue  in  their  calibration  of  the  sphere  spark 
gap  arranged  the  rotating  commutator  method  (page  627)  so 
that  very  high  voltages,  up  to  400  kv.,  could  be  dealt  with  in  the 
laboratory. 

The  charging  current  taken  by  an  air  condenser  is  rectified 
and  then  measured  by  a  critically  damped  D'Arsonval  galva- 
nometer. In  order  that  the  capacity  of  the  condenser  may  be 
accurately  calculated,  it  is  provided  with  guard  rings,  GR. 
The  two  sections  of  the  guard  ring  are  connected  together  and 
grounded  through  a  resistance,  so  that  the  difference  of  potential 
between  them  and  the  central  or  working  section  will  be  negligible 
at  all  times.  The  commutator  is  arranged  to  short-circuit  the 
galvanometer  every  alternate  half-period  and  as  the  brushes  are 
mounted  so  that  they  can  be  displaced,  the  current  may  be  thrown 
into  the  galvanometer  for  a  half-period  beginning  at  any  point 
in  the  cycle. 

The  greatest  deflection  will  be  obtained  when  the  brushes  are 
so  adjusted  that  contact  begins  when  the  voltage  is  a  positive 
maximum  (+F)  and  lasts  until  the  negative  maximum  (  —  V)  is 
reached.  If  C  is  the  capacity  of  the  condenser,  the  total  quantity 
displaced  by  the  unidirectional  current  will  be  2CV.  Then,  if/ 
is  the  frequency,  the  average  current  during  the  contact  is 

I  =  4CVf. 

The  deflection,  D2,  of  the  galvanometer,  due  to  a  steady  cur- 
rent, 72,  taken  when  the  commutator  is  running,  is 

^  DZ    =    -tV/2 

and  Z>L 

~~ 


In  order  to  obtain  correct  results,  it  was  necessary  to  do  away 
with  static  troubles  by  surrounding  all  wiring,  instruments, 
switches,  and  resistances  with  grounded  coverings  of  tin  foil  or 
with  wire  screens. 

The  condenser  used  by  Chubb  and  Fortescue  consisted  of  a  cen- 
tral cylinder  with  hemispherical  ends,  diameter  60  cm.,  length 
458  cm.  This  was  the  high-potential  "plate."  The  grounded 


700 


ELECTRICAL  MEASUREMENTS 


" plate"  consisted  of  three  sections,  as  shown,  having  a  total 
length  of  240  cm.  and  a  diameter  of  162.8  cm.  The  central,  or 
working  section,  was  47.7  cm.  long,  and  its  capacity  was  calcu- 
lated and  found  to  be  2.657  X  10~n  farads. 

The  commutator  may  be  driven  by  a  synchronous  motor. 
The  brushes  must  then  be  set  so  that  the  deflection  of  the  galva- 
nometer is  a  maximum.  If  an  induction  motor  be  used,  the 
deflection  goes  through  a  regular  cycle,  corresponding  to  the  wave 
form  of  the  voltage  applied  to  the  condenser.  The  maximum 
deflection  of  the  galvanometer  may  then  be  read. 

Whitehead  and  Gorton  in  their  researches  on  the  dielectric 
strength  of  air  replaced  the  commutator  by  an  arrangement  of 
mercury-arc  rectifiers  as  shown  in  Fig.  440. 


o  Trana. 


FIG.  440. — Whitehead  and   Gorton  arrangement  of  electrical  valves    for 
measuring  peak-voltage. 

A  mercury  arc  with  a  mercury  and  an  iron  electrode  allows 
the  current  to  flow  from  the  iron  to  the  mercury  but  effectually 
prevents  any  flow  in  the  opposite  direction. 

To  maintain  the  ionization  in  the  tubes  independently  of  the 
small  current  whose  mean  value  is  to  be  measured,  two  sources 
of  direct  current  are  used. 

The  average  value  of  the  current  is  found  by  multiplying  the 
reading  of  the  ammeter  A  by  2. 

The  use  of  electrical  valves  has  been  further  developed  by 
Chubb  in  the  switchboard  apparatus  shown  in  Fig.  441,  The 
valves  for  suppressing  alternate  half-waves  are  placed  in  the 
drawers  marked  " right"  and  "left"  and  are  seen  at  V\  and  Vz  in 
the  diagram.  The  anodes  are  of  tungsten  or  molybdenum,  the 
cathodes  of  incandescent  tungsten,  the  bulbs  being  filled  with 
mercury  vapor.  The  cathodes  are  heated  by  alternating  currents 
supplied  through  two  small  transformers,  B\  and  B^. 


CABLE  TESTING 

H 


701 


A.C.JLighting  Circuit 


B 
FIG.  441. — Chubb  peak  voltmeter,  Westinghouse  Co. 


702 


ELECTRICAL  MEASUREMENTS 


The  testing  transformer  is  operated  with  one  terminal 
grounded.  The  other  terminal,  of  the  condenser  type,  fur- 
nishes the  capacity  necessary  for  the  operation  of  the  arrange- 
ment. Variations  of  the  frequency  from  the  normal  value  are 
indicated  and  measured  by  the  frequency  meter  at  the  top  of 
the  panel. 

Referring  to  the  diagram,  Fig.  441,  it  will  be  seen  that  the  full 
potential  difference  which  is  applied  to  the  specimen  is  also 
impressed  between  the  outer  conducting  layer  of  the  condenser 
terminal  C,  i.e.,  its  outside  flange,  and  the  conductor  H.  For 


Fixed  Resistance 


FIG.  442. — Section  of  Simplex  Peak-voltmeter. 

the  first  half  wave  the  charging  current  flowing  to  the  condenser 
C  passes  through  Vi,  and  for  the  second  half  wave  through 
F2.  The  unidirectional  current  through  Vi  is  measured  by  the 
pivoted  moving  coil  galvanometer,  M,  which  is  arranged  for 
switchboard  use. 

Theoretically,  the  electrical  valves  may  introduce  a  small 
error,  for  if  the  voltage  wave  is  greatly  distorted  the  current 
flowing  to  the  condenser  may  have  negative  values  during  a  half- 
cycle.  In  order  that  the  net  value  of  the  current  flowing  through 
the  condenser  may  be  measured,  these  negative  values  should  be 
included  in  the  current  which  flows  through  the  galvanometer. 

Another  method  of  measuring  peak  voltages  is  by  the  use  of 
an  instrument  based  on  the  oscillograph  principle,  such  as  the 
Simplex  Vibrating  Voltmeter,  a  section  of  which  is  shown  in  Fig. 


INDEX 


Accuracy  and  precision,  593 
Accuracy,   percentage  of  for  watt- 
hour  meters,  defined,  493 
Ageing  of  magnets,  artificial,  34 
Agnew,  P.  G. 

tubular  electrodynamometer  for 

large  currents,  87 
comparison  method  of    testing 
instrument  transformers,  588 
Alternating  current,  measuring  large, 

86 

Aluminum,  conductivity  of,  232 
Ammeter,  54 

inclined  coil,  General  Electric,  71 
induction,  Westinghouse,  449 
moving  coil,  55 

Weston,.55 
soft  iron,.  Weston,  71 
thermo,  hot  wire,  58 
high  frequency,  61 
parallel  wire,  63 
Anderson  bridge,  403 
Astatic  electrodynamometer,  83 
Astatic  needle  system  for  Thomson 

galvanometer,  8 
Ayrton     and      Mather      universal 

shunt,  52 
Ayrton  and  Perry  inductor,  344 


B 


Balance,  current,  89 

Kelvin  or  Thomson  balance,  92 
Rayleigh  absolute  balance,  90 
advantages   of    for    absolute 
measurements,  91 


BALLISTIC  GALVANOMETER 
Chapter  II,  99 
calibration  of,  103 
checking  device  for,  102 
damped,  109 

critically  damped,  120 
description  of,  99 
movable  systems  for,  101 
reading,  precautions  in,  102 
shunts  used  with,  122 

universal  shunt,  advantage 
for    open    circuit   work, 

124 
theory  of, 

damped  instrument, 

when  e.m.f.  applied  to 
circuit  is  a  function  of 
time,  109 

when    discharge    is     in- 
stantaneous      (Equa- 
tion 20),  115 
when    discharge    is  pro- 
longed 

according  to  exponen- 
tial law,  117 
according     to      graph 
connecting  e.m.f.  and 
time,  119 
by  impulses,  118 
critically  damped  instru- 
ment,     instantaneous 
discharge,  121 
undamped  moving  coil  in- 
strument, 107 
undamped   Kelvin    instru- 

menti  109 

Best   resistance   for   Thomson   gal- 
vanometer, 17 
Blavier  test,  673 


707 


708 


INDEX 


Blondel,  A 

theorem    concerning    measure- 
ment of  power  in  polyphase 
circuits,  328 
Braun  tube,  644 
Breakdown   tests    of    high    voltage 

cables,  692 
Bristol     curve     drawing    ammeter, 

553 

Broca  galvanometer,  23 
Brooks,  H.  B. 

deflection  potentiometer,  277 
variable  inductor,  345 


C 


CABLE  TESTING 

Chapter  XV,  672 

breakdown  test  of  high  vol- 
tage cables,  692 
fault  location,  672 

in  underground  high  ten- 
sion cables,  684 
Cadmium  cell,  Weston,  298 
CALIBRATION  OF  INSTRUMENTS 
Chapter  XIII,  593 

calibration  by  standard  cell, 
ammeters,    direct   current, 

606 
voltmeters,  direct  current, 

604 
calibration  by  potentiometer, 

608 

calibration  of  ammeters  and 
voltmeters,  alternating 
current,  608 

calibration  of  wattmeters,  610 

calibration       of      watt-hour 

meters,    see   Meter   testing, 

490 
Calibration  of 

resistance   boxes    and    bridges, 

170 

slide  wire,  178 
Campbell,  A. 

compensation  for  inductance  of 
shunts,  139 


Campbell,    A.,    mutual  inductance 
measurement,  417 
standard  of  mutual  inductance, 

342 

CAPACITY  AND  INDUCTANCE,   MEA- 
SUREMENT OF 
Chapter  VII,  341 

capacity  measurement 

absolute  method,  Maxwell, 

364 
alternating  current  method, 

elementary,  380 
Anderson  bridge,  403 
bridge  method,  using  vari- 
able current,  381 
deflection  method,  369 

using  commutator,  373 
DeSauty  method,  383 
Gott  method,  377 
impedance  bridge,  390 
secohmmeter  method,  389 
Thomson  method,  375 
Wien  bridge,  393 
Capacity,  standards  of 

air  condensers,  absolute,  347 
air  condensers,  secondary,  350 
using  compressed  gas  dielec- 
tric, 353 

mica  condensers,  360 
paraffined  paper  condensers,  364 
working  standards,  354 
Chubb,  L.  W. 

analyzer,  harmonic,  666 
crest  voltmeter,  700 
Clark  cell,  294 
Closed     circuits,     measurement     of 

resistance  of  part  of,  96 
Compensation  or  lagging  of  induc- 
tion   wattmeters    and    watt- 
hour  meters 
See  Induction  instruments,  453 

Induction  watt-hour  meter,  475 
Condensers 

on  alternating  current  circuits, 

358 

on  direct  current  circuits,  357 
air,  347 


INDEX 


709 


Condensers,  capacity,  determination 
of,  364 

compressed  gas,  353 
mica,  360 

paraffined  paper,  364 
phase  angle,  determination  of, 

394 

sub-divided,  354, 
Conductivity,  see  resistivity,  227 
Conductivity 

of  aluminum,  232 
of  copper,  international  stand- 
ard, 230 
per  cent.,  232 
Conductivity  bridges,  232 

Hoopes  conductivity  bridge,  233 
Contact  method,  for  wave  form,  613 
Copper,    conductivity    of,    interna- 
tional  standard,  230 
temperature  coefficients  for,  223 
temperature  correction  for,  222 
Crest  voltmeter,  Chubb,  700 
Critical  damping 

ballistic  galvanometer,  120 
condition  for,  26 
moving  coil  galvanometer,  38 
Cross-section,     best    form     of    for 

Thomson  galvanometer  coil,  14 
CURRENT  MEASUREMENT 
Chapter  I,  1 
ammeters,  54 
current  balance,  89 
electrodynamometer,  72 
galvanometers,  1 

Current,  sources  of,  for  inductance 
and  capacity  measurements,  420 
CURVE  DRAWING  OR  GRAPHIC  RE- 
CORDING INSTRUMENTS 
Chapter  XI,  see  Graphic  record- 
ing instruments,  552 
Curve  tracer,  Rosa,  617 
Cyclograph,    for    measuring    power 
losses  in  insulation,  326 

D 

Damping 

of  ballistic  galvanometers,  109 


Damping  of  ballistic  galvanometers, 

critical,  120 
of  galvanometers,  25 

critical,  31 
D'Arsonval    galvanometer,    moving 

coil  galvanometer,  32 
critically  damped  moving  coil 

galvanometer,  38 
current    and    voltage    sensi- 
tivity of,  41 

auxiliary  damping  for,  43 
D'Arsonval-galvanometer 
described,  32 
magnetic  damping  for,  38 
magnetic     impurities    in    coil, 

effect  of,  35 
magnets  for,  34 
suspensions  for,  36 
temperature,  effect  of,  37 
Decade   and   dial   arrangements   of 

resistance  coils,  143 
Demand  indicators,  511 
General  Electric  Co. 
printometer,  525 
type  M2,  523 
type  W,  518 
Ingalls,  520 
Westinghouse  Co. 
type  R.O.,  526 
Wright,  513 
DeSauty     method     for     comparing 

capacities,  383 
Dial   and  decade   arrangements   of 

resistance  coils,  143 
Differential    galvanometer    method 
for  measuring  resistances,  157 
Kohlrausch    method,    overlap- 
ping shunts,  159 
Direct  deflection  method 

for  comparing  capacities,  369 
for  high  and  insulation  resist- 
ance measurement,  201 
for  resistance  measurement,  156 
Disconnections,  total,  locating,  690 
Drysdale,  C.  V. 

phase  shifting  transformer,  502 
phase  shifting  transformer,  290 


710 


INDEX 


Drysdale,     C.     V.,     potentiometer, 

alternating  curent,  291 
wattmeter  readings,  correction 

of,  311 
Duddell,  W. 

ammeter,  thermo,  60 
galvanometer,  thermo,  46 
inductor,  104 

Durgin,   W.   A.,   exploring  coil  for 
locating  grounds,  687 


E 


Earth  inductor,  104 

Earth  overlap  test,  674 

Einthoven  or  string  galvanometer, 

44 

ELECTRICITY  METERS 
Chapter  IX,  457 

demand  indicators,  511 
meter  testing,  490 
watt-hour  meters 
direct  current,  457 
induction,  473 
mercury,  484 
Electrodynamometer,  72 

Agnew  tubular,  for  heavy  cur- 
rents, 87 
astatic,  83 

Irwin,  84 

law  of  electrodynamometer,  77 
rewinding  of  electrodynamome- 
ter, 85 
Siemens  electrodynamometer, 

76 
Electrometers 

attracted  disc,  244 
quadrant,  248 

ELECTROMOTIVE    FORCE    AND    PO- 
TENTIAL DIFFERENCE  MEAS- 
UREMENT 
Chapter  V,  236 

see  Potential  difference. 
Electrostatic  instruments,  243 
Electrostatic  tube  for  determining 

wave  form,  647 
Electrostatic  wattmeter,  320 


Errors  in  indicating  electrical  instru- 
ments, 595 

due  to  balancing,  lack  of,  598 
to  corrosion  of  springs,  598 
to  eddy  currents,  602 
to  electrostatic  action,  602 
to  external  temperatures,  599 
to  frequency  and  wave  form, 

603 

to  friction,  596 
to  internal  heating,  600 
to  millivoltmeter  leads,  599 
to  reading,  595 
to  scale  errors,  598 
to  shunts,  598 
to  springs,  597 
to  stray  fields,  601 
to      thermo      electromotive 
forces,  599 

Evershed,  Megger,  213 

Extension  coils  for  slide  wire  bridge, 
174 


Fault  location,  672 
Blavier  test,  673 
disconnections,    locating   total, 

690 

earth  overlap  test,  674 
high    tension    cables,    locating 
faults  in  underground,  684 
Durgin     exploring     coil    for 

verification  tests,  687 
loop  tests,  676 

two  ammeter  loop  test,  676 
Fisher  loop  test,  682 

resistance  of  defective  con- 
ductor, determination  of, 
680 

Murray  loop  test,  678 
Varley  loop  test,  679 
volt-ammeter  test,  675 
Ferranti  ampere  hour  meter,  485 
Fisher  loop  test,  682 
Fleming  and  Dyke  resonator,  424 
Fluxmeter,  124 


INDEX 


711 


Foster,  G.  Carey 

calibration  of  slide  wire,  178 
comparison  of  nearly  equal  re- 
sistances, 175 

determination  of  mutual  induc- 
tance in  terms  of  capacity,  418 
FREQUENCY   METERS,    PHASE    ME- 
TERS, POWER  FACTOR  INDICA- 
TORS AND  SYNCHROSCOPES 
Chapter  X,  530 

frequency  meters,  546 

induction,     Westinghouse, 

550 
magnetic     vane,     Weston, 

551 
resonating  frequency  meters, 

546 

General      Electric      Com- 
pany, 546 
Hartmann  and  Braun,  549 


Galvanometer  constant 
denned,  3 

of    coil    of    rectangular    cross- 
section,  13 

relation  of    galvanometer    con- 
stant    to     galvanometer 
resistance,     Thomson    galva- 
nometer, 16 
Galvanometers 
ballistic,  99 

D'Arsonval,  or  moving  coil,  32 
Einthoven,  or  string,  44 
Julius  suspension  for  galvanom- 
eters, 49 
motion  of  suspended  system  of 

galvanometer,  24 
selection  of,  points  to  be  con- 
sidered, 48 

tangent  galvanometer,  1 
thermo,  46 

Thomson  or  Kelvin,  5 
General  Electric  Co. 

ammeter,  curve  drawing,  555 
ammeter,  inclined  coil,  71 


General  Electric  Co.,  demand  indi- 
cator 

type  M2,  523 
type  W,  518  t 
frequency     meter,     resonating, 

546 

power  factor  meter,  537 
wattmeter,     polyphase     curve 

drawing,  557 
wave  meter,  621 
Giebe  speed  regulator,  426 
Graded  coils  for  Thomson  galvanom- 
eter, 15 
GRAPHIC     RECORDING    OR     CURVE 

DRAWING  INSTRUMENTS 
Chapter  XI,  552 

arrangements     to     minimize 

effects  of  pen  friction,  556 
direct  acting  instruments 
Bristol  curve  drawing  am- 
meter, 553 

General      Electric      curve 

drawing  ammeters,  555 

General  Electric  polyphase 

watt-meter,  557 
relay  instruments 

Arconi,      curve      drawing 

wattmeter,  558 
Westinghouse,  curve  draw- 
ing voltmeter,  558 
uses  of,  552 
Grassot  fluxmeter,  124 
Grounds,  location  of,  672 

H 

Hartmann  and  Braun 

ammeter,  hot  wire,  59 
ammeter,  high  frequency,  69 
frequency  meter,  548 
synchroscope,  543 
voltmeter,  hot  wire,  241 

Heaviside,  O.,  bridge,  410 

Helmholtz  tangent  galvanometer,  4 

Heydweiller 

method  for  determining  mutual 
inductance  in  terms  of  capac- 
ity, 418 


712 


INDEX 


High  frequency  ammeters,  61 
High  resistance  measurement,  200 
Hoopes  conductivity  bridge,  233 
Hospitalier  ondograph,  622 
Hot    wire     ammeters,    thermo-am- 

meter,  58 

Hot  wire  voltmeters,  241 
Hughes  bridge,  408 


Idle  current  meters,  530 
Impedance  bridge,  390 

capacity    measurements    with, 

392 
inductance  measurement  with, 

399 

when  all  four  arms  are  induc- 
tive, 402 

Wien  modification  for  capacity 
and  phase  angle  determina- 
tions, 393 

Inclined  coil  ammeter,  71 
INDUCTANCE  AND  CAPACITY  MEAS- 
UREMENT 
Chapter  VII,  341 

inductance  measurement 
by  alternating  current,  ele- 
mentary method,  379 
Anderson  bridge,  403 
constant  speed  devices,  425 
impedance  bridge,  390 
Maxwell     bridge     method 
using  variable  currents, 
386 
mutual  inductance  bridge, 

408 

Heaviside  bridge,  410 
secohmmeter,  389 
sources  of  current  for,  420 
vibration       galvanometer, 

434 

Wilson  method,  using 
quadrant  electrometer, 
414 

inductances  with  iron  cores, 
measurement  of,  415 


INDUCTANCE  AND  CAPACITY  MEAS- 
UREMENT 

mutual  inductance,  measure- 
ment of,  415 
Heydweiller     and     Carey 

Foster 

mutual     inductance     in 
terms  of  capacity,  418 
standards  of  inductance,  341 
Ayrton  and  Perry  inductor, 

344 
Brooks  variable  inductor, 

345 

Campbell  standard  of  mu- 
tual inductance,  342 
variable     mutual     induc- 
tances, 343 
Maxwell  method,  416 
INDUCTION  INSTRUMENTS 
Chapter  VIII,  444 

advantages  and  disadvan- 
tages of  induction  instru- 
ments, 456 

induction  ammeters  and  volt- 
meters, 449 

effect    of    frequency    and 
temperature    on    induc- 
tion ammeters,  451 
induction  principle,  the,  444 
induction  wattmeter,  452 
lagging  device  for,  453 
see  also   Induction  watt- 
hour  meter,  475 

Induction  watt-hour  meters,  473 
lag  adjustment,  475 
light  load  adjustment,  478 
sources  of  error  in,  478 
frequency,  480 
temperature,  479 
voltage,  482 
wave  form,  481 
Ingalls  demand  indicator,  520 
Instruments 

absolute,  denned,  1 
secondary,  defined,  1 
Insulation  resistance,  200 

direct  deflection  method,  201 


INDEX 


713 


Insulation  resistance,  insulation  re- 
sistance of  commercial  circuits 

with  power  on,  214 
loss  of  charge  method,  209 
Megger,  Evershed,  213 
voltmeter  method,  208 
Irwin    astatic   electrodynamometer, 
84 


Julius  suspension,  49 


K 


Kelvin  or  Thomson  balance,  92 
Kelvin  or  Thomson  double  bridge, 

191 

best  resistance  for  Thomson 
galvanometer,  used  with, 
195 

galvanometer  current  in,  194 
precision  measurements  with, 

198 
Reeves  method  for  adjusting 

ratio  arms,  199 
sensitivity    attainable    with, 

196 

Wenner  method  for  eliminat- 
ing lead  resistances,  199 
Kelvin  or  Thomson  galvanometer,  5 
Kohlrausch 

method  of  overlapping  shunts 
for  resistance  measurements 
using  differential  galvanom- 
eter, 159 


Lag  adjustment  for  induction  watt- 
hour  meters,  475 

Lag  coil  for  commutating  watt-hour 
meters,  471 

Leeds  and  Northrup  potentiometer, 
274 


Leeds  and  Northrup  speed  regu- 
lator, 430 

Lincoln  synchroscope,  540 

Load  boxes  for  meter  testing,  494 

Logarithmic  decrement,  30 

Loop  tests,  676 

Low  resistances,  measurement  of, 
190 


M 


Magnetic  damping  for  moving  coil 

instruments,  38 
Magnetic  shielding,  8,  22 
Magnetic   vane   ammeter  and  volt- 
meter, 70 
Magnetic     vane     frequency    meter, 

551 
Magnets 

ageing  of,  34 
cast  iron,  34 

temperature  coefficient  of,  34 
Manganin  resistance  wire,  129 
Maximum  demand  indicators,  511 
Maxwell,  J.  C. 

absolute  measurement  of  capac- 
ity, 364 

comparison      of     inductances, 
386 

of  mutual  inductances,  416 
Megger,  Evershed,  213 
Mercury  motor  meters,  484 
ampere-hour  meter,  485 
Ferranti,  485 
Sangamo,  487 

watt-hour  meter,  Sangamo,  488 
Meter  testing,  490 

ficticious    loads    and    arrange- 
ments   for     phase    shifting, 

500 

load  boxes,  494 
methods  of  testing,  493 
phase      shifting      transformer, 

Drysdale,  502 
portable     standard     watt-hour 

meters,  495 
sources  of  error  in  meters,  493 


714 


INDEX 


Meter  testing,  testing  large  direct- 
current  watt-hour  meters, 
506 

polyphase     induction     watt- 
hour  meters,  504 
timing    device    for    calibrating 

watt-hour  meters,  499 
Mica  condensers,  360 
Microphone  hummer,  422 

Campbell  form,  423 
Motion  of  suspended  system  of  gal- 
vanometer, 24 

Moving  coil,  or  D'Arsonval  galva- 
nometer, 32 
Murray  loop  test,  678 
Mutual  inductance,  measurement  of, 

415 
Carey  Foster  and  Heydweiller 

method,  418 
Maxwell  method,  416 
Mutual  inductance  bridge,  408 

effect  of  eddy  currents  in,  412 
Mutual  inductance  standards,  341 


N 


Needle    system    for    Thomson    gal- 
vanometer, 11 
Northrup,  E.  F. 

alternating    and  direct-current  i 

comparator,  610 
measurement  of  insulation  re- 
sistance with  power  on,  214 

O 

Ondograph,  Hospitalier,  622 
Oscillograph,  629 

electrostatic,  641 

theory  of,  638 


Paraffined  paper  condensers,  364 
Parallel  wire  ammeter  for  high  fre- 
quency current,  63 
Peak  or  crest  voltage,  measurement 
of,  698 


Peak  Chubb,  crest  voltmeter,  700 
Simplex  peak  voltmeter,  702 
Phase  angle  of  condensers,  denned, 

358 
determined    by    Wein    bridge, 

394 

Phase    angle    of   instrument   trans- 
formers, 566 

current  transformers,  582 
potential  transformers,  587 
Phase   angle   and   ratio   corrections 
due     to     instrument     trans- 
formers, 577 

effect  of  phase  angle  in  three- 
phase  power  measurements, 
578 

PHASE  METERS,  POWER  FACTOR  IN- 
DICATORS,      SYNCHROSCOPES 
AND  FREQUENCY  METERS 
Chapter  X,  530 
frequency  meters,  546 
idle  current  meters,  530 
phase  meter,  532 
polyphase    power   factor    in- 
dicators, 536 
power  factor  charts,  539 
single-phase  power  factor  in- 
dicators, 535 
synchroscopes,  540 
synchronizing  lamps,  543 
Phase  meter,  Tuma,  532 
Poggendorf  method  of  comparing  a 
potential  difference  and  an  elec- 
tromotive force,  269 
Polarity  tests  for  instrument  trans- 
formers, 570 
Polyphase,  circuit,  measurement  of 

power  in,  328 
wattmeter,  333 
watt-hour  meter,  482 
POTENTIAL  DIFFERENCE  AND  ELEC- 
TROMOTIVE FORCE  MEASURE- 
MENT 

Chapter  V,  236 
electrostatic  instruments,  243 
potentiometer       arrangements, 
269 


INDEX 


715 


POTENTIAL  DIFFERENCE  AND  ELEC- 
TROMOTIVE FORCE  MEASURE- 
MENT 

potentiometer       arrangements, 
potentiometer,  271 

alternating  current,  289 
deflectional,  277 
Leeds    and    Northrup    po- 
tentiometer, 274 
thermo  kraft  frei,  284 
Wolff  potentiometer,  276 
voltmeters,  for   direct  current, 

236 

for  alternating  current,  239 
electrostatic,  253 

Potentiometer  method  for  measur- 
ing resistance,  157 
Potier,  method  for  measuring  power, 

320 

Power  factor  charts,  539 
POWER  FACTOR  INDICATORS,  PHASE 
METERS,         SYNCHROSCOPES 
AND  FREQUENCY  METERS 
Chapter  X,  530 
single-phase  power-factor  in- 
dicators, 535 

polyphase  power  factor  indi- 
cators, 536 

POWER  MEASUREMENT 
Chapter  VI,  303 
cyclograph,  326 
instrument  transformers  used 
in     power      measurement, 

565 

polyphase  circuits,  measure- 
ment of  power  of,  328 
Potier     method     for     power 

measurement,  320 
power      diagram      indicator, 

Ryan,  326 

split    dynamometer    method 

for  power  measurement,  319 

three  dynamometer  method, 

317 

voltmeter  method,  318 
wattmeter,  electrodynamo- 
meter,  304 


POWER  MEASUREMENT 

electrostatic,  320 

polyphase,  333 

Puriga  power  factor  meter,  539 
Pyrometer,  resistance,  224 

Q 

Quadrant  electrometer,  248 
Quartz  fibers,  11 

R 

Rate  of  watt-hour  meters,  defined, 

493 
Rayleigh 

Clark  cell,  296 
current  balance,  89 
Reeves  method  for  adjustment  of 

Thomson  bridge,  199 
Resistance  coil,  construction  of,  128 
for    alternating    current  work, 

133 

RESISTANCE  DEVICES 
Chapter  III,  128 
resistance  boxes,  142 

dial   and   decade   arrange- 
ments, 143 

multiple    decade    arrange- 
ments, 144 

Northrup  decade  arrange- 
ments, 145 
resistance    coil,    construction 

of,  128 
for      alternating      current 

work,  133 
rheostats,  145 

RESISTANCE  MEASUREMENT 
Chapter  IV,  155 

closed  circuit,  resistance  of  a 

part  of,  95 
commercial       circuit       with 

power  on, 

Northrup  method,  216 
voltmeter  method,  214 
deflection  method,  156 
differential  galvanometer,  157 
Kohlrausch  method,  159 


716 


INDEX 


RESISTANCE  MEASUREMENT 

high    and    insulation    resist- 
ances, 200 
direct    deflection    method, 

201 

loss  of  charge  method,  209 
Megger,  Evershed,  213 
voltmeter  method,  208 
low  resistance  measurement, 

190 
Kelvin  bridge,  Thomson  or, 

191 
Wheatstone  bridge  method, 

190 

potentiometer  method  for 
resistance  measurements, 
157 

substitution  method,  156 
volt  ammeter  method,  155 
Wheatstone  bridge,  162 
slide  wire  form,  172 
Resistance  pyrometer,  224 
Resistance  standards,  131 

low   resistance   for   alternating 

current  work,  137 
compensation  for  inductance 

of,  139 
national  physical  laboratory 

form,  140 

Reichsanstalt  form,  137 
Resistance  wire,  manganin,  129 
Resistance  of  part  of  permanently 
closed  circuits,  measurement  of,  95 
Resistivity,    conductivity,    methods 

of  stating,  227 

aluminum,  resistivity  of,  232 
copper,     resistivity     of,     inter- 
national standard,  230 
per  cent,  conductivity,  232 
Resistivity    temperature    constant, 

230 
and  temperature  coefficient  of 

resistance,  231 

Resonator,  Fleming  and  Dyke,  424 
Rheostats,  145 

carbon  compression,  153 
immersed  wire,  150 


Rheostats,  water,  145 
wire,  150 

Rosa,  E.  B.,  curve  tracer,  617 

Rotary  standard  watt-hour  meter, 
portable  standard  watt-hour  me- 
ters, 495 

Ryan,  H.  J.,  power  diagram  indi- 
cator, 326 


S 


Sangamo 

ampere-hour  meter,  487 

watt-hour  meter,  488 
Secohmmeter,  389 
Self  inductance,  measurements,  see 
•Inductance  and  capacity,  meas- 
urement of,  341 

standards,  344 
Sensitivity  of  galvanometer 

ampere,  microampere,  20 

megohm,  22 

normal,  21 

volt,  microvolt,  21 
Shielding,  magnetic,  8,  22 
Shunts,  51 

Ayrton  and  Mather  universal, 
52 

for  ballistic  galvanometer,  122 

low  resistance,  for  alternating- 
current  work,  137 

switchboard,      for      ammeters, 

57 
Siemens  electrodynamometer,  76 

setting  up  of,  77 
Siemens  and  Halske 

synchronizing  lamps,  544 

voltmeter,  high  range,  258 
Slide  wire,  calibration  of,  178 

bridge,  172 

Soft  iron  instruments,  69 
Solenoidal  inductor,  106 
Spark  gap 

needle  point,  260 

A.I.E.E.  table  for,  261 
humidity  effect  on,  263 

sphere  gap,  263 


INDEX 


717 


Spark  gap,  sphere 

A.I.E.E.  table  for,  267 
correction    for    density    and 

temperature  of  air,  267 
Speed  controllers 
Giebe,  426 

Leeds  and  Northrup,  430 
Wenner,  432 
Split     dynamometer     method     for 

measuring  power,  319 
Standard  cells,  294 
Clark  cell,  294 
board  of  trade  form,  295 
H  form,  296 
materials  used  in  standard  cells, 

297 
precaution    in    using    standard 

cells,  300 
Weston      or      cadmium      cell, 

298 
Weston     secondary     cadmium 

cell,  300 

Star  box  or  Y  box,  338 
Stray    currents,    measurement    of, 

94 

String  galvanometer,  Einthoven  gal- 
vanometer, 44 
Stroude  bridge,  407 
Substitution  method  for  measuring 

resistance,  156 
Suspensions 

for     Thomson     galvanometer, 

10 

strip,    for     D'Arsonval    galva- 
nometer, 36 

Synchronizing  lamps,  543 
SYNCHROSCOPES,     PHASE     METERS,. 
POWER   FACTOR   INDICATORS 
AND  FREQUENCY  METERS 
Chapter  X,  530 

Hartmann    and    Braun   syn- 
chroscope, 543 
Lincoln  synchroscope,  540 
synchronizing  lamps,  543 
Siemens  and  Halske,  syn- 
chronizing lamps,  544 
Weston  synchroscope,  542 


Temperature  coefficient  of  electrical 

resistance,  218 

mean  temperature  coeff  cient,221 
temperature    coefficient    of    re- 
sistance, 221 

coefficients  for  copper,  223 
correction  for  copper,  222 
Thermo,  ammeters,  58 

e.m.f.,     compensation     for     in 

Wheatstone  bridge,  172 
galvanometer,  Duddell,  46 
Thomson  or  Kelvin  balance,  92 
double  bridge,  191 
galvanometer,  5 
watt-hour  meter  for  direct  cur- 
rent, 457 
Three     dynamometer    method    for 

measuring  power,  317 
voltmeter  method  for  measuring 

power,  318 

TRANSFORMERS,  INSTRUMENT 
Chapter  XII,  562 

current  transformer,  563 
theory  of,  572 
ratio  and  phase  angle  ex- 
perimentally    deter- 
mined,  580 

by  comparison  test,  588 
polarity  tests  for,  570 
potential  transformer,  562 
theory  of,  575 
ratio  and  phase  angle  ex- 
perimentally       deter- 
mined, 584 

by  comparison  test,  588 
Tubular  electrodynamometers,   Ag- 

new's  for  heavy  currents,  87 
Tuma  phase  meter,  532 
adjustment  of,  534 
application    to    polyphase    cir-, 

cuits,  536 

Two  wattmeter  method  for  measur- 
ing polyphase  power,  331 
Y  box  for  use  with  balanced 
loads,  338 


718 


INDEX 


U 

Units,  legal  electrical  in  U.  S.,  705 
Universal  shunt,  Ary ton  and  Mather, 
52,  202 

V 

Varley  loop  test,  679 
Vibration  galvanometer,  434 
current,  sensitivity  of,  436 
voltage,  sensitivity  of,  438 
Voltmeter 

•alternating-current,  239,  241 
direct-current,  236 

effect  of  temperature  on,  237 
electrodynamometer  voltmeter, 

239 

hot  wire  voltmeter,  241 
Hartmann  and  Braun,  242 
roller,  242 
induction,  449 
electrostatic,  253 

condenser  multiplier  for,  256 
high  range,  258 
use  of  false  zero,  256 
Volt-ammeter  method  for  resistance 

measurement,  155 
Vreeland  oscillator,  420 

W 

Wagner  earth  connection,  397 
Walker,  Miles,  connections  for  elec- 
trostatic wattmeter,  321 
Water  rheostats,  145 
Wattmeter 

electrodynamometer,  304 

designation  of  terminals   of, 

329 
heating  losses  in,  306 

compensation   for   heating 

in  potential  circuit,  307 
local  field  effects,  308 
mutual   inductance   between 
current  and  potential  cir- 
cuits, effect  of,  315 
reactance  in  potential  circuit, 
effect  of,  309 


Wattmeter  ,  electrodynamometer, 
reactance  in  potential 
circuit,  compensation  for, 
313 

correction  for,  311 
voltage    between    fixed    and 

movable  coils,  309 
electrostatic  wattmeter,  320 
induction  wattmeter,  452 
lagging  device  for,  453 
polyphase  wattmeter,  333 
interference   of   elements   of, 

333 
Wattmeter   method   for   measuring 

large  alternating  currents,  86 
Watt-hour  meter  „ 

accuracy,  relative,  of  induction 
and  commutating  types  under 
service  conditions,  468 
commutating  meters  for  direct 

current,  457 

on  alternating  current  cir- 
cuit, 471 

essential  characteristics  of  watt- 
hour  meters,  461 
induction      watt-hour      meter, 
473 

lagging  device  for,  475 
polyphase,  482 

mercury  watt-hour  meter,  488 
meter  testing,  490 
three  wire  meter  for  direct  cur- 
rent, 469 
Wave  analysis,  650 

Fischer-Hinnen  method,  661 
harmonic  analyzers,  666 
Chubb  analyzer,  666 
Laws  method  of  experimental 

analysis,  669 
Runge     method     of     grouping 

terms,  652 
example  of  12  point  schedule, 

656 

WAVE  FORM,  DETERMINATION  OF 
Chapter  XIV,  612 
Braun  tube,  644 
contact  method,  613 


INDEX 


719 


WAVE  FORM,  DETERMINATION  OF 
electrostatic  tube,  647 
integrating  methods,  624 
oscillograph,  629 
theory  of,  638 
electrostatic,  641 
Wave  meter,  General  Electric  Co., 

621 
Wenner,  F. 

adjustment  of  Thomson  bridge, 

199 

speed  controller,  432 
Westinghouse 

demand  indicator,  RO,  526 
frequency  meter  induction,  550 
harmonic  analyzer,  666 
power  factor  meter,  538 
voltmeter,  curve  drawing,  558 
Weston 

ammeter,  moving  coil,  55 
frequency  meter,  551 
soft  iron  instruments,  71 
standard  cell,  298 
synchroscope,  542 
voltmeter,  moving  coil,  236 
wattmeter,    polyphase    correc- 
tion for  interference  of  ele- 
ments, 333 
Wheatstone  bridge,  162 

best    position    for    galvano- 
meter, 185 


Wheatstone  bridge,  best  resistance 
for  Thomson  galvanometer 
used  with,  184 

bridge  tops,  examples  of,  167 
calibration  of  bridge  or  resist- 
ance box,  170 
compensation        for        large 

thermo  e.m.f.,  172 
galvanometer,  current  in,  183 
sensitivity    attainable    with, 

187 
Wheatstone  bridge,   slide  wire 

form,  172 

extension  coils  for,  174 
Whitehead    and    Gorton,    arrange- 
ment for  measuring  peak  voltage, 
700 

Wien  bridge,  for  determining  capac- 
ity and  phase  angle  condenser,  393 
Wilson,   method  for  measuring  in- 
ductance, 414 


Y  box,  star  box,  for  use  in  measure- 
ment of  balanced  three-phase 
power,  338 


Z 


Zeleny,  discharge  key,  372 


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